IMITATIVE RESEARCH AND DEVELOPMENT IN THE NEO-
SCHUMPETERIAN THEORY OF GROWTH
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
This dissertation would not be possible without the experience, enthusiasm and
generosity of many. Elias Dinopoulos provided valuable guidance and made many
course corrections along the way. Richard Romano and Doug Waldo contributed
essential perspective on style, presentation, and logical consistency. Each, by example
and advice, also introduced me to the art of teaching. Peter Thompson often played the
devil's advocate, forcing me to rethink and refine my arguments. I thank these people
for their assistance and many others who helped in my studies.
TABLE OF CONTENTS
ABSTRACT ......................................... .vii
1. IMITATION IN GROWTH AND TRADE
1.1 Introduction ...................... ..... ...... 1
1.2 A Stability Consideration .... .. ................6
1.3 Imitation and Trade Among Advanced Countries .......... 8
1.4 Imitation and International R&D Knowledge Spillovers ...... 10
2. STABILITY IN NEO-SCHUMPETERIAN MODELS OF GROWTH
2.1 Introduction ..............
2.2 Introducing Specific Factors .
2.2.1 The Model .............
184.108.40.206 Consumer behavior ....
220.127.116.11 Asset market ........
18.104.22.168 Production and entry .
22.214.171.124 Research and development
126.96.36.199 Innovation ..........
188.8.131.52 Imitation ...........
2.2.2 Market Equilibrium .......
184.108.40.206 Product market .......
220.127.116.11 Labor market.........
18.104.22.168 Specific factors .......
2.2.3 Steady-State ...........
22.214.171.124 Characteristics .......
126.96.36.199 Industrial targeting ...
188.8.131.52 Zero-profit conditions .
184.108.40.206 Steady-state equilibrium .
. . . 13
. . . 15
. . . .15
. . . .17
. . . .18
. . . 18
. . . .20
. . . 2 1
. . . 2 1
. . . .22
. . . .22
. . . .23
. . . 23
. . . .24
. . . .24
. . . 24
. . . 25
. . 26
. . . .27
2.3 Stability and Comparative Statics ................... .28
2.3.1 Stability ................ ................. 29
2.3.2 Comparative Statics ................... 34
2.4 Restrictions and an Example . . ... 35
2.4.1 Restrictions .............................. 35
2.4.2 Example ............... ...............37
2.5 Conclusion ................................37
3. ENDOGENOUS INTERNATIONAL TECHNOLOGY TRANSFER
AMONG ADVANCED COUNTRIES
3.1 Introduction .......................... .......39
3.2 World Economy ................ .......... .42
3.2.1 Overview ............................. 42
3.2.2 Consumer Behavior ................... ... ..43
3.2.3 Product Markets ......................... 43
3.2.4 Innovative R&D ......................... .44
3.2.5 Imitative R&D ........ .................. .45
3.2.6 Labor Market ........................... 46
3.2.7 Industrial Targeting ......................... 47
3.2.8 Steady-State Equilibrium ................. .47
3.3 Welfare and Comparative Statics ................... .. 53
3.4 Trade and Technology Transfer .................... .55
3.4.1 Assumptions/Trading Framework ............... 55
3.4.2 Factor Price Equalization Set ................... .59
3.4.3 Trade Patterns ................... ......... 62
3.5 Conclusion .................................67
4. INTERNATIONAL R&D KNOWLEDGE SPILLOVERS
4.1 Introduction ... .................. ............69
4.2 W hat Are Spillovers? ...........................72
4.3 Acquired Knowledge Or Spillovers? ................. 76
4.4 Measuring Spillovers .......................... 85
4.5 Conclusion ............................... 89
5. WHAT'S NEXT ? .................... .... ........ 91
A. CONSUMER PROBLEM ........................... 96
A.1 Derivation of Equation 2.3 ..... ............ 96
A.2 Derivation of Equation 2.4 .................... 98
B. DERIVATION OF COBB-DOUGLAS UNIT COSTS ......... 100
C. PROOF OF STEADY-STATE CHARACTERISTICS ........ 102
C.1 Chapter2 ................................ 102
C. 1.1 Proof that Quality Leaders in a Industries Won't
Engage in Innovative R&D ...................... 102
C.1.2 Proof that a Quality Leader in a 0 Industry Will Not
Innovate ................................... 104
C. 1.3 Proof that a Previous State-of-the-Art Quality Producer
Does Not Have an Incentive to Engage in Innovative R&D in
an a Industry ...................... ......... 105
C. 1.4 Proof that a Previous State-of-the-Art Quality Leader
Will Have No Incentive to Innovate in a 0 Industry. ........ 105
C. 1.5 Proof that a Competitive Fringe Firm Will Not Engage
in Innovative Activity in an a Industry .............. .105
C.2 Chapter 3 .................................... 106
C.2.1 Proof that Quality Leaders in a Industries Won't
Engage in Innovative R&D ......................107
C.2.2 Proof that a Competitive Fringe Firm Will Not Engage
in Innovative Activity in an a Industry ... ........ 108
C.2.3 Proof that Quality Leaders Will Not Innovate in a 0
Industry ......................................... 109
C.2.4 Proof that Previous Quality Leaders Will Have No
Extra Incentive to Innovate ................. .. 109
D. PROPERTIES OF REDUCED FORMS ................. 111
D.1 Chapter2 .... ..... ............. ........... 111
D.1.1 Properties of C (I) ..................... .... 112
D.1.2 Properties of C (I) ..........................112
D.1.3 Intercept Terms for Figures 2.2 and 2.3 .......... .113
D.2 Chapter3 .............. ................... 114
D.2.1 Characteristics of I = 0 ................... .114
D.2.2 Characteristics of C = 0 ..................... .115
D.2.3 Comparison of Co and C, .................... 115
D.2.4 Characteristics of Czc(I) ................... 116
E. DERIVATION OF PHASE DIAGRAMS ................ 117
F. COMPARATIVE STATICS ..........................119
F.1 Subsidy to Innovation ................. .........119
F.2 Subsidy to Imitation .............. ....... ......... 120
G. WELFARE ANALYSIS .................. ........121
G.1 Derivation of the Growth Rate of Instantaneous Utility ..... 121
G.2 Derivation of Welfare ......................... 122
G.3 Welfare Properties of the World Economy ............. .122
H. ENDOWMENT REGIONS ................. ........ 126
BIOGRAPHICAL SKETCH ........................... ........ 135
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
IMITATIVE RESEARCH AND DEVELOPMENT IN THE NEO-SCHUMPETERIAN
THEORY OF GROWTH
Chair: Elias Dinopoulos
Major Department: Economics
This dissertation explores endogenous technology transfer through imitation. The
context is a dynamic general equilibrium model of growth generated by innovation.
Segerstrom extends the one-factor quality ladders model of Grossman and Helpman by
incorporating endogenous imitation. Comparative static experiments produce perverse
results. An increase in a subsidy to innovative (or imitative) activity reduces the level
of innovative (or imitative) activity. In Chapter 2. I show that Segerstrom's model is
unstable because of linear research and development (R&D) unit costs. This instability
causes the perverse results.
By introducing specific factors to innovation and imitation. I obtain instantaneous
diminishing returns to R&D technology at the aggregate level, while still allowing for
constant returns to scale at the firm level. I then derive sufficient conditions for stability
requiring a certain level of instantaneous diminishing returns to R&D activity. The
satisfaction of these conditions assures the 'usual' comparative static results of subsidies
to either type of R&D: an increase in a subsidy to innovative (or imitative) activity
increases innovative (or imitative) R&D activity.
In Chapter 3, I develop a one-factor general equilibrium model of global growth.
I analyze trade among advanced countries in a two-country, integrated equilibrium, world
economy. Risky and costly imitation is the only channel of technology transfer across
countries. The patterns of trade and technology transfer fluctuate stochastically in each
industry and exhibit product cycles and endogenous two-way international technology
transfer. These trade and transfer patterns depend on relative national labor endowments.
I investigate the relevance of knowledge spillovers for theory and policy in
Chapter 4. and examine the struggle of recent empirical efforts to measure the magnitude
and extent of spillovers. These studies do not distinguish between research efforts aimed
primarily at incremental improvements (or imitation) and R&D directed at being first to
bring out the next major product line (or innovation). As a result, they may produce
biased estimates of spillovers from foreign R&D. I argue that intraindustry technology
(or ,.nowl Icdee) transfers are aLgre.sit el acquired rather than passively 'spilled.'
IMITATION IN GROWTH AND TRADE
[Ijf we can learn about government policy options that have
even small effects on the long-term growth rate, then we
can contribute much more to improvements in standards of
living than has been provided by the entire history of
macroeconomic analysis of countercyclical policy andfine-
runiing. Economic growth ... is the part of macroeconomics
that really matters.
Barro and Sala-i-Martin (1995, p.5)
Nature moves inexorably forward, renewing, refining, replacing--so does
humanity. From the first rudimentary scraping knifes and the taming of fire to the
Hubble telescope and the splitting of the atom, we never cease our search for a better
way to get what we want, or more of it. We have more and better things every year.
In the language of economics, this is growth. It has been a staple of economic study
since the days of Adam Smith. This field, dominated by Neoclassical growth theory for
years. is enjoying a current renaissance, the focus shifting from analyzing capital
accumulation to understanding technological change.
The Neoclassical theory of growth is based on the Solow (1956) Swan (1956)
neoclassical production function model, as integrated with Ramsey's (1928) treatment of
household optimization by Cass (1965) Koopmans (1965).' It predicts a per-capita
growth rate that converges, in the long run. to an exogenous rate of technical change.
Neoclassical growth theory provides the comforting assertion (to the Neoclassical
economists) that the competitive outcome is Pareto optimal. In fact. there is no
government policy tool that would increase the long-run growth rate in the Neoclassical
model. The Neoclassical theory also explains several empirical stylized facts, including
per-capita output growing over time. physical capital per worker growing over time, and
conditional convergence in growth rates of output (conditional on such factors as initial
human capital levels, government policy, and trade policy).-
The Neoclassical growth theory has some key weaknesses, however. The long-
run growth rate of per-capita income is explained solely by exogenous technical change--
that mysterious little black box. Also, Neoclassical growth theory does not satisfactorily
explain large differences in living standards, development experiences, and growth rates
across countries. Comparison of the East Asian Tigers to the countries of Sub-Saharan
Africa leaves the strong impression that, contrary to the dictates of Neoclassical theory.
government economic policy and trade regime do matter. These weaknesses, combined
with technical advances in mathematical modelling (e.g., imperfect competition).
encouraged the assault on neoclassical growth theory by endogenous growth theory.
'For full treatments of the Neoclassical theory of growth, see the relevant chapters
in Barro and Sala-i-martin (1995), Blanchard and Fischer (1992), or Grossman and
"See Barro and Sala-i-Martin (1995. Ch 1.2)
The objective of the new growth theory is not to describe the mechanics of growth
but to explain its causes. Thompson provides these criteria for endogenous growth
C.1. Endogenous growth models must permit a non-
zero long-run rate of per-capita welfare growth.
C.2 The long-run rate of growth must be a function of
choice variables in the model. (1994, p.l)
There are three main knowledge-based engines of the new growth theory: The
human capital accumulation model (as most recently popularized by Lucas ) bases
growth on the individual decisions of agents investing in education. Learning-by-doing
models (Romer , Lucas , ) envision improvements in technique as a
result of accumulated production experience. Finally, there are models that explain
growth as an outcome of investments by firms in research and development (R&D).
It is a subclass of the latter type of endogenous growth model--Neo-
Schumpeterian--which is the focus of this dissertation. Solow suggests that
the real value of endogenous growth theory will emerge
from its attempt to model the endogenous component of
technological progress as an integral part of the theory of
economic growth. (1994, p.51)
The Neo-Schumpeterian theory of growth aspires to exactly this. Its name arises because
it formalizes Schumpeter's (1942) view of creative destruction as the engine of growth.
Creative destruction is the process by which new goods are brought to the market.
eroding the profits of producers of older goods.
Schumpeter's ideas have been studied at the microeconomic level for some time.
The most useful models for adaption to general equilibrium models of growth are the
stochastic R&D race models of Loury (1979), Dasgupta and Stiglitz (1980a,b), Lee and
Wilde (1980), and Reinganum (1985). These models capture the formal investment
activities in research and development by firms attempting to maximize profits, the
uncertain nature of such investments, and the prospect of winners and losers in
contestable markets. General equilibrium models of monopolistic competition, such as
that of Dixit and Stiglitz (1977). provide a vehicle for integrating these models into
growth theory. An early endogenous growth model along this line is that of Grossman
and Helpman (1989): successful innovators discover new varieties of goods, increasing
consumer utility over time. Since goods are imperfectly substitutable, however, no good
is ever replaced.
The first dynamic general equilibrium models to capture the process of creative
destruction are those of Segerstrom. Anant, and Dinopoulos (1990) and Aghion and
Howitt (1992). Elements of these two models are incorporated into a quality ladders
model by Grossman and Helpman (1991b). Innovations are modeled as Poisson
processes. There is free entry into stochastic R&D races in each industry. One winner
discovers how to produce a product of superior quality. Concurrent races across a
continuum of industries result in a certain and continuous growth rate of aggregate
consumer utility. As Thompson (1994) points out. market externalities in these models
move the competitive equilibrium away from the socially optimal outcome. An
appropriability effect occurs, whereby the innovator cannot capture all social benefits:
an intertemporal spillover effect exists because the benefits of an innovation last forever.
but the firm doesn't. An R&D subsidy or tax can achieve the socially optimal outcome.
but there is no consensus on which is needed.
A second prominent feature of technical change to consider is technological
diffusion--particularly imitation. Baldwin and Scott distinguish between imitation and
dissemination--voluntary technology transfer by the innovator (say through licensing):
Unauthorized imitation is a major diffusion mechanism
when patents are easily circumvented, when high litigation
costs and uncertainties make patents little more than a
"license to sue," and when "reverse engineering," or the
analysis of how a competitor's product was made, is
routinely pursued. Imitation may in some circumstances
augment the net social benefits from innovation by
speeding diffusion and expanding an innovation's ultimate
spread toward the output level where the marginal social
cost of adoption equals the marginal social benefit. But,
alternatively, by reducing anticipated earnings, imitation
may retard the incentive to innovate. (1987. p. 120)
This concept has also been studied in depth at the microeconomic level. Some of the
important theoretical works which sought to understand the relationship between market
structure, innovation, and imitation were Scherer (1967). Kamien and Schwartz (1978)
and Nelson and Winter (1982). These efforts have uncovered a variety of possible
strategic situations: market power may encourage or inhibit imitation and imitation may
foster or discourage market concentration.
Several key empirical case studies by Mansfield et al. (1981), Mansfield et al.
(1982), and Mansfield (1985) conclude that imitators typically take 70 percent of the time
and spend 65 percent as much on R&D as the innovator; imitation lags are between one
and two years; patents raise the costs of imitation but don't reduce its occurrence: the
expectation of rapid imitation does not discourage innovative activity: and cross-country
imitation lags may be declining due to improvements in communication, transportation.
and the increased relative importance of more easily imitated products such as software.
Imitation is an important phenomenon.
Several Neo-Schumpeterian models of growth encompass the possibility of
imitation. These are, almost exclusively, two-country models that examine various issues
of North-South trade. The primary model is Grossman and Helpman (1991b). In their
model, only the North innovates: the South gains market share by imitating and captures
the market because of lower wages. This model was generalized and used to examine
such issues as property rights protection (Helpman . Taylor [1993a,b], )
and. partial market penetration (Glass ). Far less work examines imitation and
trade between advanced countries. One exception, incorporating exogenous imitation into
a Heckscher-Ohlin model with endogenous innovation, is Dinopoulos et al. (1993). One
of the goals of this dissertation is to endogenize imitation in a model of trade between
advanced countries. I regard this as an essential step in understanding the role of
technology transfer at all stages of world development.
1.2 A Stability Consideration
Segerstrom (1991) develops a closed economy Neo-Schumpeterian model of
endogenous innovation and endogenous imitation. The difficulty in endogenizing
imitation is the necessity of positive expected economic profits in final goods production
to provide motivation for the potential imitator to enter into costly and risky imitative
activity. In the North-South model, this is simply a matter of postulating differences in
production capabilities across countries. It is a little more difficult in a closed-economy
model. Segerstrom proves the existence of a steady-state Nash equilibrium in which
imitators can expect to collude with the market leader and earn positive profits. I extend
this model to a two-country version in which technology transfer occurs through
endogenous imitation. First, however, a stability analysis proves necessary.
In Segerstrom's model, innovation and imitation are modelled as Poisson
processes: there is free entry into both innovative and imitative R&D races, there is one
factor of production, and unit labor requirements in each activity are constant. This
model, however, has unusual comparative static results: a subsidy to innovation lowers
the per industry level of innovative activity. Concurrently, a subsidy to imitation lowers
imitative activity. In Chapter 2, I show that this arises from the assumption of constant
unit labor requirements. By introducing specific factors to each activity, I allow for
instantaneous diminishing returns to R&D and show that. when there are sufficient
diminishing returns, the comparative static results are reversed: a subsidy to innovation
increases the level of industry innovative activity. Similarly, a subsidy to imitation
increases the level of imitative activity.
In the spirit of Samuelson's Correspondence Principle. I relate the above result
to a stability analysis. I introduce ad-hoc adjustment mechanisms. These require entry
into or exit from R&D races when expected discounted profits are not equal to expected
discounted costs, as required for equilibrium. I find that, when instantaneous diminishing
returns to R&D are not sufficient, the model's only interior solution is locally unstable.
This necessity of diminishing returns accords with several empirical studies. See
Thompson (1995b) for an empirical study of. among other things, instantaneous returns
to R&D in a Neo-Schumpeterian model. He finds strong evidence for diminishing
returns. As it turns out, introducing diminishing returns to R&D imposes no great
limitation on the usefulness of the models involved. I incorporate instantaneous
diminishing returns into the two-country model of Chapter 3 of this dissertation, and
study the implications of endogenous imitation for trade patterns.
1.3 Imitation and Trade Among Advanced Countries
Trade economists have long preached the virtue of free trade, but empirical
studies have usually reported only minor static welfare losses resulting from trade
restrictions.3 The new growth theory may validate the trade theorists' policy
recommendations, however, with the possibility of large dynamic effects of trade policy.
Romer (1993b) shows that, in a country where lifting trade restrictions can introduce
new goods into the economy, the potential welfare benefits are an order of magnitude
larger than traditional welfare loss measurements. Trade restrictions can also reduce the
size of potential profits to innovation, lowering the rate of innovation and growth.
3See Feenstra (1992) for a discussion of the empirical measurement of welfare
Another benefit of the new growth models is the ability to explain changing trade
patterns over time. The North-South trade models formalize Vernon's (1966) description
of the product cycle. Production of new goods, introduced in the North, is eventually
transferred to the South to take advantage of lower production costs. Dinopoulos et al.
(1993) develop a dynamic version of the two-country Heckscher-Ohlin model. Growth
is driven by endogenous innovation, and trade patterns are influenced by innovation and
exogenous imitation. Interindustry and intraindustry trade, product cycles and
multinationals are possible, but technology transfer is exogenous, costless, and can only
occur in one direction, contrary to the evidence.4
Chapter 3 extends the model of Chapter 2 to a two-country integrated equilibrium
world economy in which factor price equalization occurs. The model is simplified by
assuming that there is now only one factor of production. Each R&D activity has a
specific functional form exhibiting instantaneous diminishing returns to R&D. There is
also an exogenous diffusion effect, introducing the possibility that imitative R&D activity
has a positive welfare effect aside from any competitive or variety effects in the final
goods market. Technology transfer can only occur through costly imitation. Two-way
technology transfer and trade patterns depend on relative national labor endowments.
4See the various studies by Mansfield cited above and the survey of Nadiri (1993),
which enumerate the expenses incurred in efforts to transfer technology from one country
to another, both cooperative and noncooperative.
1.4 Imitation and International R&D Knowledge Spillovers
With the advent of endogenous growth literature, R&D knowledge spillovers have
come to play an important role in growth theory. Long-run growth in utility.
productivity or per-capita income is still driven by technological Jhange. but
technological change is endogenized in the Neo-Schumpeterian literature. It arises from
investment in R&D. But, are there long-run diminishing returns to R&D, as there are
to additions to the capital stock?5 Formal Neo-Schumpeterian modelling generally side-
steps this question by assuming that, in the steady-state, the expected costs of discovering
each new higher quality product are no larger than the expected costs of discovering the
last. Each new increment in knowledge is achieved at constant cost. This assumption
of constant returns to scale (CRS) in R&D is justified by the notion that there are
spillovers of knowledge from current innovations that aid in subsequent innovations and
exactly offset any long-run diminishing returns. There is no attempt to identify the
mechanisms by which these spillovers are accomplished.
In addition to the importance of spillovers in long-run growth. Neo-Schumpeterian
literature also assigns importance to them in interactions among countries. Generally,
anything which increases the profitability of national R&D increases growth. Thus, the
5These long-run diminishing returns to R&D should be distinguished from the
instantaneous diminishing returns to R&D discussed above. The former occurs, for
example, if a given stock of basic knowledge offers a fixed amount of exploitable ideas.
Although basic research is often considered to have nondecreasing long-run returns ( See
Romer [1993b]), it may or may not accumulate fast enough to counteract diminishing
returns to the current stock. Instantaneous diminishing returns can occur at the industry
level if there are fixed factors, such as skilled labor, in R&D activity.
importance of free trade comes to the forefront of policy discussions because of the large
potential growth effects of increases in market size. It is also true that policies which
increase the effectiveness of accessing foreign knowledge, thus increasing the
productivity of home R&D efforts, will accelerate growth." These may or may not be
free trade policies. Whatever the case, it seems advisable to delve deeper into the
nature of international R&D knowledge spillovers.
Recent empirical literature tries to quantify the magnitude and extent of
international R&D spillovers. Two key related questions are at the center of attention:
Is there a significant geographic dimension which may imply advantage to the country
of origin for any given innovation? What is the relative contribution to. say, productivity
growth of domestic and foreign R&D efforts? Griliches (1992) surveys the literature and
concludes that R&D spillovers are both prevalent and important. Nadiri (1993), in an
extensive survey, concurs, citing evidence that finns must incur R&D expenses to realize
the benefits of knowledge spillovers, and presenting findings that spillovers may be
stronger within than among countries. Irwin and Klenow (1994). however. present
evidence that spillovers flow freely across borders. Coe and Helpman (1993) conclude
that spillovers to trading partners amount to 25 percent of the world return to R&D
conducted by the seven largest OECD economies. A ubiquitous finding of this type of
"See Dinopoulos and Kreinin (1994), Ruffin (1994) and Brecher. Choudri and
Schembri (1994) for examples of models that exhibit this effect.
7Irwin and Klenow's study looks at the semiconductor industry because it is
considered a strategic industry. The study uses data on average industry selling price and
firm shipments. The findings on spillovers lead the authors to conclude that there is no
justification for a national R&D subsidy to that industry.
study is that foreign R&D has a stronger total effect on factory productivity than
The theoretical implications of the model developed in Chapter 3 suggest a more
complex relationship between trade and international R&D knowledge spillovers than
implied by most existing studies. In particular, the model implies that some R&D
expenditures are innovative and some imitative. I argue in Chapter 4 that ignoring this
difference introduces bias into estimates of the magnitude of spillovers, and leads to
misinterpretation of the relative contributions of foreign and domestic R&D. I first
discuss the concept of spillovers in depth, stressing the need for engaging in R&D
activity in order to capture true spillovers of knowledge from the R&D activities of
others. I next develop an equation of knowledge accumulation and technology transfer
consistent with the model of Chapter 3 and compare it to some existing literature. The
chapter concludes with some thoughts on the measurement of spillovers.
STABILITY IN NEO-SCHUMPETERIAN MODELS OF GROWTH
The new growth literature is experiencing a few growing pains. Economists' use
of new mathematical tools opens up new modeling possibilities unparalleled in traditional
Solovian growth models, yet the simplifying assumptions which make these models
workable sometimes lead to trouble. Devereux and Lapham (1994), for example, discuss
a stability problem in the knowledge-driven model of new product innovation of Rivera-
Batiz and Romer (1991). A branch of Neo-Schumpeterian growth theory, beginning with
the work of Grossman and Helpman (1991b), has a similar stability problem. This
chapter shows that introducing instantaneous diminishing returns to R&D activity resolves
the stability problem.
Recall from Chapter 1 that Segerstrom (1991) extends Grossman and Helpman's
(1991b) model of quality growth. He incorporates endogenous innovative and imitative
R&D activities into a closed-economy one-factor model of growth. It is one of two Neo-
Schumpeterian models of growth incorporating endogenous imitation.' The model
generates counter-intuitive comparative static results: when a subsidy to innovative R&D
SThe alternative is the product cycle model of Grossman and Helpman (1991a).
is introduced, the intensity of innovative activity falls. The same is true of a subsidy to
This chapter shows that these perverse comparative-static results arise because
the model is unstable. The problem is the use of linear R&D unit costs. By introducing
a more general cost function. I show that the instability can be eliminated and the unusual
comparative static results reversed. This occurs when there are sufficient instantaneous
diminishing returns to R&D. Segerstrom (1994) and Cheng and Tao (1993) address
similar issues. Segerstrom shows that the quality ladders model of Grossman and
Helpman (1991b) is not stable when all industries are not subsidized and uncertainty
about which industries will be subsidized exists. Cheng and Tao replace the linear costs
of Segerstrom (1991) with quadratic costs and show that this reverses the comparative
static results. They do not conduct a stability analysis or derive stability conditions.
This chapter looks explicitly at the relationship between the stability analysis and the
comparative static results.
Section 2.2 sets out the model and establishes the existence of equilibrium
(Proposition 1). Section 2.3 examines the stability of the model and develops the
connection with the comparative static results of subsidies to innovation and imitation
(Proposition 2). Section 2.4 provides a numerical example. A final section offers
2.2 Introducing Specific Factors
2.2.1 The Model
This is a dynamic general equilibrium model with a final goods sector and an
R&D sector. Quality-improving innovations occur stochastically over time in a
continuum of industries producing final goods. These, in turn, augment utility because
firms cannot appropriate all of the returns to innovation. A representative agent has a
Cobb-Douglas instantaneous utility function with perfect substitutes (CDP). The agent
maximizes utility over time and over the continuum of final goods. Profit-maximizing
firms use consumer savings to hire labor and undertake R&D.
There are two types of R&D, both of which are modeled as Poisson processes.
Costly and risky innovative R&D is undertaken in each industry, under conditions of free
entry, by firms hoping to be the first to discover the next highest-quality product and
enjoy temporary monopoly profits. Following this innovation, costly and risky R&D is
undertaken in each industry to copy the latest state-of-the-art product. The firm learning
how to duplicate the product first is able to share collusive profits with the leader in the
industry. Growth in consumer utility is endogenously generated by firms choosing R&D
There are three factors of production. Production of final goods exhibits CRS
in labor. Entry into final goods production, however, requires the successful acquisition
of knowledge (innovation or imitation). In addition to labor, the production of innovative
activity requires a fixed specific factor, capital, as does the production of imitative
activity.2 Both factor markets are competitive, and CRS prevails in both R&D activities.
In the presence of fixed factors, however, both innovation and imitation will exhibit
aggregate industry instantaneous diminishing returns to R&D.
In the steady state, consumer expenditures, the interest rate, and the percentage
of industries with one quality leader are constant. The intensities of innovative and
imitative activity are also constant. Innovation and imitation are exponentially distributed
events. The pace of these events is governed by the constant intensity of R&D efforts.
In the steady-state equilibrium, the market structure of each industry alternates between
a monopoly targeted for an imitation race and a duopoly threatened by an innovation
race. Although the current quality leaders) capture the entire market in each industry.
producers of previous state-of-the-art goods force limit pricing on the monopolist and/or
There are R&D knowledge spillovers from innovation to imitation because the
unit costs of imitation are always lower in the steady state than the unit costs of
innovation. There are also exogenous R&D spillovers from one product cycle to the next
because the expected costs of successively larger innovations stay constant. These
spillovers will be discussed, in depth, in Chapter 4. In the next several pages, the
model is briefly developed.
'That innovation and imitation activity may have specific capital in the short run has
support in the literature. It is often different types of firms that innovate and imitate.
See Baldwin and Scott (1987). See also Jovanovic and MacDonald (1994) who argue
that innovation and imitation are substitutes in that firms may compete for market share
by either method.
220.127.116.11 Consumer behavior
A continuum of final goods industries is indexed by w E [0,1]. Each industry
has an countably infinite number of potential qualities, j =0.1 ..., increasing in j. Only
a subset of these qualities has been, as yet, discovered at time t. A representative
infinite-lived consumer maximizes lifetime utility, given by
U fe '"z(t)dt (2.1)
with subjective discount rate p and instantaneous utility
z(t) JI.n Iy XJd(w) dw (2.2)
in which d,,(w) is the quantity consumed at time t. in industry o, of quality j. The
measure of quality improvement of the j* quality over the j-l" quality is X, which is
greater than one by assumption. Let h,(w) represent the state-of-the-art quality at time
t in industry w. Then, it increases utility relative to the lowest quality available by Ah
Because of the stochastic nature of innovation, ht(w) will vary across industries.
As indicated in the next subsection, the current quality leaders) can always
capture the market by charging a limit price determined by its degree of quality
advantage because, given equal quality-adjusted prices, the consumer is assumed to
choose the highest quality available. The instantaneous demand function maximizes
instantaneous utility for given instantaneous expenditures. E(t):
E(t if j h,(o)
d,.(m) Pi,(W) (2.3)
The price, at time t. of the j' quality in industry w, p,,(w). is taken as given by the
consumer. The time path of expenditure that maximizes lifetime utility is
Aggregate expenditure is determined in the steady state by the value of assets, and r(t)
is the instantaneous interest rate. Equations 2.3 and 2.4 are derived in Appendix A.
18.104.22.168 Asset market
In the asset market, savings are supplied to firms to finance R&D expenditures.
In a typical R&D race, each firm issues a stream of Arrow-Debreu securities for the
duration of the race. The proceeds are just enough to cover the firm's R&D
expenditures. Each security pays out the expected discounted profits of the successful
firm, contingent on the firm winning the R&D race at the instant the security is issued,
and zero otherwise. Since there is a continuum of industries, the industry-specific
uncertainty involved with R&D can be eliminated by the consumer who invests in
diversified mutual fund portfolios. In the steady-state equilibrium, the instantaneous
interest rate equals the riskless rate.'
22.214.171.124 Production and entry
As the name implies, a property of the CDP utility is that. at equal quality-
adjusted prices ( pi,()/ 1 pi,())/l' ), consumers are indifferent to the various
available qualities within an industry. Assume that indifferent consumers will always
choose the higher quality. Take labor as the num6raire so that w = wage = 1. Since
'See Dinopoulos (1994) for a detailed explanation of the asset market in these types of
previous quality producers are willing to supply at marginal cost (p= 1), current leaders
can only markup the price by as much as the consumer values the current quality over
the previous quality. A price higher than X is never optimal since the within-industry
price elasticity of demand is infinite, meaning the consumer would switch entirely to the
lower quality. So, p = X in each industry at all times in the steady state. Appendix C
shows that, in this model, an industry leader never leads by more than one step up the
quality ladder because leaders never innovate. This is not as unreasonable a
characteristic, empirically, as it sounds because, as discussed below, this is a model of
Final goods production is such that one unit of output is produced by one unit of
labor for all products and qualities. To produce the final good, however, firms must
learn how to do so by investing in R&D and winning innovative R&D races. The first
firm to innovate in industry a becomes the sole producer in that industry. This industry
is then targeted for an imitative R&D race. The winner will learn how to copy the
production method of the latest quality product and collude with the current leader.4 The
next round of innovative R&D races will result in discovery of the next quality level, a
new industry leader and so on.
'Segerstrom(1991) proves that a Nash equilibrium steady state exists in which imitators
collude with quality leaders in the production of final goods and so can expect to make
positive profits. The latter is required for costly imitative R&D activity to exist. This
specification of imitation is made for simplicity. An alternative specification in which
imitation is in the form of horizontal differentiation is taken up in Dinopoulos (1992).
126.96.36.199 Research and development
By engaging in i (or c) units of innovative (or imitative) activity each moment.
a firm 'buys' the probability idt (or cdt) of successfully carrying out the next innovation
(or imitation) in the industry in the interval dt. I (or C) is the total level of innovative
(or imitative) activity in each industry targeted for innovation (or imitation) at each
moment.5 Idt is the constant probability that. if the innovation does not occur by time
t. it will by time t + dt. The time duration of each R&D race is exponentially
distributed in the steady state: the hazard rate is the intensity of R&D activity (I or C).
Innovation and imitation races in each industry are subject to free entry, which will occur
until expected discounted profits are driven to zero.
The specific factors in R&D are not specific to an industry but to a particular
activity--innovation or imitation. This implies aggregate diminishing returns to each
activity. Since there is a continuum of industries. no one industry (or firm) is large
enough to affect the returns to the specific factors. All industries are identical, however.
so a representative industry can be thought of for which the specific factor is fixed in the
steady state. This is because the fixed endowment of each specific factor is employed
equally among the fraction of industries .targeted for innovation or imitation. In the
steady state this fraction is constant. Firms are atomistic in each industry at this stage
and can hire labor and capital freely. The number of firms cni aged in R&D is
indetenninant. but not the number of producers.
'To avoid cumbersome notation, and because I and C are constant in the steady state.
I and C are not explicitly shown to be functions of time.
Labor employed in innovative activity in each industry is L, K, is capital
employed, and I is the intensity of innovative activity for the representative industry
targeted for innovation. Production can be described by the unit cost function. Let w,
be the return to capital, aL the unit labor requirement. and aKI the unit capital
requirement (w,, aU, and aK, are shown, in Appendix B. to be functions of I). Firms are
assumed to be atomistic. capital is fixed, and a Cobb-Douglas production function is
adopted for convenience. Appendix B derives the following expression for unit costs:
lI 1 LI w adKI l," (2.5)
In equation 2.5, 0 is labor's share in innovative costs, and a,, defined in
Appendix B, is a function of parameters and K,. Intuitively, aggregate per-industry
capital is fixed. As I rises, the return to K, rises relative to that of the mobile factor,
L,. Thus, au, /aI = (du, /dw,)(aw, /lI) > 0. The advantage of introducing specific
factors is that. even though production at the firm level exhibits CRS. the representative
industry (or economy-wide aggregate innovative activity) is subject to diminishing
The amount of labor employed in imitation is Lc, Kc is the level of capital, and
C is the aggregate level of imitative activity for the representative industry subject to
imitation. Let wc be the return to capital in imitation, aLc be the unit labor requirement.
and aKC be the unit capital requirement (we, aLc and aKC are functions of C). With finns
small, with capital fixed, and with a Cobb-Douglas production function, unit costs are
lc aLC WCaKC ;c.CC' (2.6)
In (2.6), (c 1 -y is labor's share in imitation costs. and ac, defined in Appendix
B, is a function of production function parameters and K(. Hence. auc /3C = (du.
idwc)(9wc /lC) > 0.
2.2.2 Market Equilibrium
188.8.131.52 Product market
Because the total number of industries is of measure one. consumer demand in
each industry is given by (2.3). As noted, quality leaders can capture the market by
charging p = X. A quality leader has a constrained monopoly in equilibrium, and the
monopoly profits are given by
L (X E(t) I l E(t) (2.7)
in which (X-1) is the markup and E(t)/X is quantity demanded in each market. After
imitation occurs, there are two quality leaders who collude. continue to charge price p
= X and divide the market equally. Profits to each are
rc 1 E (2.8)
An important implication of the foregoing discussion is that price is constant over time
and across industries. Collusion turns out to be a fairly convenient method of allowing
for positive expected profits to imitation.
184.108.40.206 Labor market
Labor is homogeneous, the economy has an endowment of L, and the labor
market clears at each moment in time. Labor demand comes from three sources--
production, imitative R&D, and innovative R&D. Since one unit of labor produces one
unit of final product, the demand for labor, at time t, in final goods production equals
E(t) The unit labor requirement for innovation is au, so aLI is the labor demand for
innovative R&D, at each time t, in each industry targeted for innovation. Similarly,
aLcC is the labor demand for imitative R&D, at each time t, in each industry targeted for
imitation. Let 0(t) be the fraction of industries (duopolies) targeted for innovation, and
a(t) be the fraction of industries (monopolies) targeted for imitation. Total R&D labor
demand is 3(t)aaL I oa(t) aLC C. The full employment condition, at time t, is (using (2.5),
(2.6), and the definitions of aLc and aLl in Appendix B)
L E(t) (t)aLlI ()aLC E(t) +e a,(t) ".* yaCa(t) C'l. (2.9)
220.127.116.11 Specific factors
The returns to capital. w, and wc, adjust to ensure that the aggregate amount of
each specific factor (K, K,) is always fully employed. The full-employment conditions
K, aKI P(t) K, K,/I(t) (2.10)
and Kc aKCCa(t) Kc Kc/a(t) (2.11)
2.2.3 Steady State
This paper considers a symmetric Nash equilibrium steady state in which
consumer expenditures and the proportion of industries with one quality leader are
assumed to be constant over time. However, since the focus is on the equilibrium
levels of I and C, an equivalent representation of the steady state is developed. The
model is reduced to two equations in I and C. Segerstrom (1991) and Segerstrom and
Davidson (1991) show that innovators will collude with one and only one imitator and
that quality leaders will not collude with previous state-of-the-art producers. This is true
In2>(p ( I') Assumption Al"
In < pA Assumption A2
S> max 3 Assumption A3
In Assumptions A2 and A3, A is the lag before a cheater can be detected violating the
collusive agreement and punished.7
6The denotes a steady-state value.
7In Chapter 2, Assumption Al can be satisfied by choosing the labor endowment
sufficiently small such that I* is small enough to satisfy the inequality. In Chapter 3.
with I' always less than one, Assumption Al will be satisfied if 1n2 > 2pA. This
inequality and Assumption 2 allow a range of A which satisfy the model. Assumption
A3 can be satisfied, for given A and p, by a sufficiently large quality increment. This
is a model that considers large innovations.
The steady state has the same characteristics as Segerstrom (1991): . E and
a are constant over time, by assumption; . r(t) = p which follows from
characteristic . and equation 2.4: . I (or C) is constant across time and industries
targeted for innovation (or imitation), by the assumption of symmetry, the fact that price
is constant across time and from characteristic , above: . One quality leader earns
rL, as shown in equation 2.7, and two quality leaders earn re, as shown in equation 2.8:
. There are only two types of industries--those with one leader and those with two
leaders: . In industries with one leader. there is no innovative R&D and previous
quality leaders don't imitate; . In industries with two quality leaders, there is no
imitative R&D and, neither current nor previous leaders innovate. Characteristics  -
, listed above, are proven in Appendix C.
18.104.22.168 Industrial targeting
Since innovation (or imitation) is governed by a Poisson process. in an interval
of time. dt. an industry becomes an a (0) industry with probability Idt (Cdt). The
proportion of industries becoming a industries in dt is flIdt. The proportion of
industries becoming 3 industries in dt is a Cdt. So, 3 = 1 a and &(t) obeys
&(t) = (1 -a(t))I(t) a(t)C(t) (2.12)
In the steady state, &(t) =0, so aCdt = 3Idt and
aC (1 a)l a L /3 C (2.13)
The number of industries changing from one to two quality leaders) equals the number
of industries changing from two to one leaderss.
22.214.171.124 Zero-profit conditions
Expected discounted collusive profits in the steady state are
x e 17-77
v7 re t"dt le '-dr "c
in which p = r(t) is used. The random time until the next innovation, 7, is exponentially
distributed. Let s be the random time until imitation. The expected discounted benefits
to engaging in imitative activity are
bc = (Ce -c)ve I'ds Cvc
0 (p QC)
Total costs at t are unit cost times C. so the expected discounted costs from engaging in
imitative activity are
ucCe 'sds Ce dt C
recalling that Uc is as given in equation 2.6. Combining these two gives expected profits
from engaging in imitative activity and the zero-profit-in-imitation-condition is
vc t uc (2.14)
The ZPC (zero-profit condition) in innovation is developed in a similar manner.
Innovators, however, have two components to profits. From the point of innovation until
the point of imitation, the innovator earns profits 7L given in equation 2.7. After
imitation, the innovator shares the market with the successful imitator. Because 7, the
time duration of the imitation race, is exponentially distributed, v, the expected
discounted reward from innovating is
v I j L T.e 'dt e '"vc Ce -dr (TrL c)
o (p, C
Analogous to imitation, the ZPC for innovation is
v u (2.15)
126.96.36.199 Steady-state equilibrium
The next step is to reduce the model to two equations in C and I and examine the
steady-state equilibrium of the model. To obtain a steady-state labor market condition,
use (2.13) in (2.9):
I E E
L C aLl 1LC aL cC (a aLC (2.16)
IC IIC A I +C X
By substituting for E from (2.8) and for -rc from (2.12), the equilibrium labor
(2 1)L (aLl aLC)- (I)uc (2.17)
This equation implicitly defines C as a function of I. denoted CL(I). The properties of
CL(I) are derived in appendix D. CL(I) is negatively sloped with a positive intercept.
This equation is graphed in Figure 2.1 (for k4 > 0).
The Unique Steady-State Equilibrium
To obtain a steady-state ZPC in R&D. combine (2.7), (2.8), (2.14) and (2.15):
(2(p t I) i C) uc
ut (2 (2.18)
Equation 2.18 defines C,(I), the equilibrium ZPC in R&D. If three conditions--R. R2.
and R3, derived in Appendix D--hold, C,(I) will be positive and positively sloped.
Restriction RI is discussed in section 2.4. Restrictions R2 and R3 are equivalent to the
stability conditions derived in the next section. C,(I) is also graphed in Figure 2.1. and
it's properties are derived in Appendix D. The following proposition summarizes this
The Nash Equilibrium steady state represented by F in Figure 2.1 exists and is unique.
2.3 Stability and Comparative Statics
Samuelson (1983) explains the duality between stability analysis and meaningful
comparative static results, which he calls the Correspondence Principle. To apple\ this
principle, one postulates an adjustment process, presumably based on rational economic
behavior, whereby the equilibrium condition is achieved. Then, one ascertains under
what conditions, after a small disturbance, this process returns the economy to
equilibrium. This is Samuelson's "stability analysis of the first kind in the small." (1983.
258) Samuelson shows, as I do below in this case, that these stability conditions rule out
perverse comparative statics.
I will consider only local stability. Recall that unit costs for innovation and
imitation are u1 a I" and uc acC', respectively. At 0 = 4 = 0 (E= 7y = 1), the
model reduces to Segerstrom's (1991) model. At 6 = 0 = 1 (c = y = .5), the model
corresponds in reduced form behavior to Cheng and Tao (1993). First. I demonstrate
that. at 0 = 0 = 0, the model has no stable interior equilibrium. Then, I derive
stability conditions for the general model.
The transitional behavior of the state variable. c(t), will depend on the adjustment
of industry innovative and imitative activity (see equation 2.14) in response to nonzero
profits. To analyze the behavior of this model in the neighborhood of the steady state.
assume that the intensities of industry innovation and imitation obey the following
i(t) (v, u,) (2.19)8
((t) F(v. u ,). (2.20)
in which *(0) = F(0) = 0 and I'(), F'(-) > 0. The functions 'I and F convey
continual entry into (or exit from) R&D races whenever expected profits are > (<) 0.
For stability, this behavior must return the model to the steady state, in which C = 0 and
I = 0. after a disturbance. Because this model has specific capital, the adjustment rules
can be thought of as being based on capital movements with adjustment costs in response
to rental differentials, as in Neary (1982). This paper examines local stability, so it is
'The denotes a time derivative.
enough to see that a rental differential would occur (w, w,). By the 'magnification
effect' of Jones (1971), in a three factor model, the change in relative expected benefits
is always trapped between the returns to specific factors. So, for example, a small
increase in v, from F will cause a rental differential in favor of innovative capital.
Substituting into (2.19) from (2.5), (2.7), (2.8), (2.14), (2.15), and (2.16) gives
i(t) = 0 in terms of I and C:
(P. -1) IC 1 _, arl"(P [)(piC)
l)(L (Ceal yacC'' 2(2.21)
2 lC '' 2(p I)iC
Substituting into (2.20) from (2.6). (2.8), (2.14). and (2.16) gives C(t) = 0. which is the
same as (2.17) in the specific Cobb-Douglas form:
(X I) (eIC l" I YacC' ac C'(p I) (2.22)
2 I[ C
The slopes of these two functions are derived below and shown to be less than zero for
all nonnegative 0, ).
When 0 = 6 = 0. C = 0 and I = 0 can be graphed as in Figure 2.2. The values
of the various intercepts are given in Appendix D. But when ,. b are large enough.
as I show below.C > C and i =0 and C = 0 can be graphed as in Figure
dl l, dl c o
2.3. The values of Co and I0 are given in Appendix D. Comparison of Figures 2.2 and
2.3 shows that i = 0 cuts C = 0 from below in Figure 2.2 and from above in Figure
2.3. Using (2.21) and (2.22), it is straightforward to show that, in either case. for given
C, I above i = 0 implies i < 0 and vice versa. Similarly, for given I. C to the right
of C = 0 implies C < 0 and vice versa. These arguments are derived in Appendix E
and are indicated by the arrows in each phase diagram.
The Unstable Case
The Stable Case
It is apparent that F in Figure 2.2 is not locally stable. To find the stable
equilibria in the case of E = 7 = 1, the extremes of the model are examined. A
disturbance away from F to the northwest will imply C oo. I 0 and then, since all
a industries will be eventually imitated, C 0.' This means that I = C = 0, the no-
growth trap of Aghion and Howitt (1990), is one stable equilibrium. It is stable because
a disturbance away from (0,0) would require I > 0 first. Since only a countable number
of industries would experience innovation at any given point in time, C oo in those
industries and innovative activity would cease. As C 0 to the southeast of F. I -> C
and 3 0. When C = 0, innovators are no longer in danger of imitation, but are
threatened by further innovation. Then v, = rL/(p+I), C = 0, and I = (Tr/ai) p
(which equals I, in Figure 2.2) is the second stable equilibrium when 0 = =0.
In contrast, F in Figure 2.3 is a unique, interior, locally stable equilibrium. So.
for the model to be locally stable, it must be that > in absolute value in the
dl i-_o dI 0I
neighborhood of F. By differentiating (2.21) and (2.22) and comparing these slopes at
the steady-state equilibrium, it is possible to derive the restrictions on 0 and 4 such that
local stability occurs. Differentiating (2.21) and (2.22) gives
0(p+l)al" 1(p C) + acC 1!'l
dC (2(p +1)C)j (2.23)
dl aI(p (p +)(p 21)+
(2(p 1) C)2
"As C increases and I decreases, a falls and ever fewer industries are subject to
innovation and this process accelerates over time. As a -* 0, C oo. Because each
industry is infinitesimal, it is possible to have C -*oo in an individual industry even if
L is finite.
X + acC'
IY + (ac.C"^ (p l)
(Notice that (2.23) and (2.24) are negative.) In (2.23) and (2.24),
X = -1) C2 (Eal"
Y ) (Ea yacC"') IC ya C6'
2 ( C)2 ICC C
Stability can be assured if
(O(p+D)al-I(p+C)) a acC'O-C'
2(pI -1) C
acC(- > a1l(pe2I)
(2 a. ^ I )
(2( p 1) QC)
with one or both holding with strict inequality. By substituting from (2.18) for (p+C)/
(2(p+I)+C) and cancelling terms, (2.25) reduces to 0 :2 21 /(2(p+I)+C), which holds
0 2 I or <- .
By rearranging (2.26),
a > a1 c C
a, a" ( tp -C)J a
and since the bracketed term is less than one. and the term in parentheses is at most V/
by (RI), given on page 35 below, then,
4 '/2 ory <- (SC2)
(SC1) and (SC2) are sufficient conditions for stability so long as at least one holds with
strict inequality. These require sufficient diminishing returns to innovation and imitation.
Why are diminishing returns so important? Examination of the ZPCs. (2.14) and
(2.15), provides an answer. In a partial equilibrium sense, in any industry where profits
are positive, it must be that free entry into that market drives them to zero. Otherwise.
entry continues unabated, and the ZPC is never satisfied. In this model, free entry does
not directly lower the expected benefits so it must raise costs. Suppose that a disturbance
causes v, > u,. If u, is constant, the only way to reequate (2.14) is for C to rise since
av,/aC < 0. Operating through the labor constraint. I falls. If u, increases only slowly
with I then v, might rise faster than u, as I rises, widening the gap. This is because I
rising makes vc fall so that vc < uc. C falling in response (by a relatively larger amount
the less ui rises with C) will increase v,, possibly more rapidly than u,. Profits would
increase and equilibrium would not be reestablished. If there are sufficient diminishing
returns to scale in R&D (i.e., (SC1) and (SC2) hold), then u, rises more rapidly than v,
as I rises and this reequates expected profits to zero.
2.3.2 Comparative Statics
It follows directly from the stability analysis that the comparative static results
depend on whether (SCI) and (SC2) hold. Suppose the government gives a lump sum
per unit subsidy to innovative R&D. It is not difficult to show that a small subsidy will
shift I up in Figures 2.2 and 2.3 resulting in a lower I and higher C in Figure 2.2 and
a higher I and lower C in Figure 2.3. A subsidy to C will also shift C out, increasing
C and decreasing I if the model is locally stable. Intuitively, perverse comparative static
results in the neighborhood of F are eliminated when the model becomes locally stable.
This is the Correspondence Principle. Comparative static results are derived in Appendix
F. The discussion in this section leads to the following proposition:
When there are sufficient instantaneous decreasing returns to each R&D activity
((SC1) and (SC2) hold), the model is stable and the comparative static results of subsidies
to R&D activity are as e.\pecteld: a subsidy to innovative activity increases I, and a
subsidy to imitative activity increases C. Wie~ n there are not sufficient instantaneous
decreasing returns to each R&D activity ((SC1) and ((SC2) don't hold), the model is
unstable, and the comparative static results are reversed.
2.4 Restrictions And An Example
2.4 1 Restrictioins
Here I discuss the various parameter restrictions. It is shown in Segerstrom
(1991) that X large enough and L small enough to satisfy Assumptions A1-A3 are
required. In the previous section, 0 > 1 and 6 > 2 were shown to be sufficient for
stability. There is one other inequality which must hold in the steady state for a well-
behaved model. This restriction, (RI), must hold for C > 0, I > 0 (See Appendix D):
2> a > (RI)
This restriction implies that the model requires partial diffusion of product
technology from innovators to imitators. It also limits the cost advantage that imitation
has, relative to innovation. One way to ensure that (RI) holds is to assume that specific
capital is mobile in the long run and that the economy is in long-run equilibrium at F in
Figure 2.1. The return to capital will then be equalized across sectors, and there will
be a relationship between the 'price' or expected benefit ratio, the wage/return to capital
ratio, and the capital/labor ratios of the two activities, as described by the Samuelson
diagram in Figure 2.4. Assume that L is the total labor available to R&D in the steady
state and that innovation is capital intensive relative to imitation (y > E). Then,
0 CD OD
V(.\VI = U(,\UI
The Range of uc\u,
IuI Ac L1
uc e Ai Kc Y
where Ac and A, are the general coefficients of the Cobb-Douglas production functions
for imitation and innovation, respectively, defined in Appendix B. By examination of
Figure 2.4, it should be apparent that, for an appropriate choice of e, y, A,, and Ac
(which position the two functions in the top quadrant), choosing K. the total
economy endowment of capital, for given L (already restricted above), can limit the
range of u,\Uc (EF in Fig. 2.4).
It remains to show an example in which (RI) holds and the model is well-
behaved. Let L = 1, K = 2, e = /4, y = '. Ac = 2, A, = 1, X = 4, and p = .05.
Then 0 = 3, satisfying (SC1) and
Cobb-Douglas functions of Appendix B, the range of w, = w, in the long run is (1. 1 /2z)
the range of u, is then (1.76. 2.378), and the range of uc is (.95, 1.238). Then the range
of ui/uc is (1.857. 1.921), satisfying (RI). Using (2.17) and (2.18), C' = 1.93 and I'
= .83 when w, = w = 1, and C* = 1.94 and I* = .94 when w, =wc=11/2. This is
one example where all restrictions of the model are satisfied.
I have used Samuelson's Correspondence Principle to develop stability conditions
for a generalized version of the Neo-Schumpeterian growth model of Segerstrom (1991).
Innovation and imitation are endogenously determined in a dynamic. zero-profit, general
equilibrium model of growth in consumer utility through quality improvements. Each
R&D activity uses labor and specific capital. Standard adjustment mechanisms, supported
in principle by the work of Neary (1982), are used in the stability analysis. I show that
sufficient instantaneous decreasing returns to scale in R&D are required for a well-
behaved model in which the comparative static results are reasonable.
The implication for future work is that the inclusion of separate R&D sectors in
a dynamic general equilibrium model with levels of R&D activity determined by free
entry and zero-profit conditions imposes restrictions on the structure of the model. The
mathematical sophistication of Segerstrom's model disguises the stability problem. but
an appeal to Samuelson's analysis clarifies the issues.
ENDOGENOUS INTERNATIONAL TECHNOLOGY TRANSFER
AMONG ADVANCED COUNTRIES
A photograph snapped at a fashion show in Milan can be faxed
overnight to a Hong Kong factory, which can turn out a sample in
a manner of hours. That sample can be fedexed back to a New
York showroom the next day.
Wall Street Journal 8-8-94
Imitation of new products or processes is an increasingly important avenue of
technology transfer in the global marketplace. In the U.S., it is estimated that sixty
percent of patented innovations are imitated within four years.' Furthermore. among
advanced countries, the rate of international technology transfer through imitation
depends on R&D investment.: Finally, technology transfers flow in all directions among
'Mansfield et al. (1981), pg. 913. This paper investigates, through case studies, the
magnitude and determinants of imitation costs and the relationship of these costs to
innovation costs, the imitation time lag, patents, and entry.
2Mansfield et al. (1982), pg. 35. Based on data from 37 innovations in the plastics.
semiconductors, and pharmaceutical industries, this study also concludes that imitation
lags appear to be decreasing over time.
advanced countries.3 Japan spends resources to copy U.S. technology in semiconductors
and automobiles, but U.S. companies also try (with limited success) to transfer Japanese
technology (i.e. quality circles) to the U.S.4
Several endogenous growth models include various aspects of the complex
dynamics of imitation. First, Segerstrom, Anant and Dinopoulos (1990) and Dinopoulos.
Oehmke and Segerstrom (1993) model imitation as an exogenous, certain and costless
activity. These studies explore the effects of changes in the imitation lag on innovation
and growth. Second. Grossman and Helpman (1991a) develop a model of North South
trade in which the South engages in endogenous imitation based on expected profits from
lower manufacturing costs, which result in a lower wage. None of the models mentioned
above endogenizes imitation among advanced countries with identical wages. Nor do any
generate multidirectional patterns of endogenous international technology transfer.
To that end, this chapter develops a two-country model of growth based on the
introduction of new products of higher quality. This model is closely related to that of
Chapter 2. Endogenous innovation and endogenous imitation influence both consumer
utility and trading patterns. To simplify the analysis, I assume that there is only one
factor of production, labor. Instantaneous diminishing returns to R&D. essential for
'See Eaton and Kortum (1994) and Coe and Helpman (1993). The first study, using
data on patents, productivity, and research in five leading research economies, reports
that, for each country, more than 50 percent of productivity growth is attributable to
foreign technology. The second study, using data on 22 OECD countries, finds that
international R&D spillovers to trading partners accounts for about one quarter of the
total social return to the R&D investment of the seven largest OECD economies.
4Dinopoulos and Kreinin (1994) report that U.S. companies spent $950 billion, in the
period 1983-1993, in an attempt to implement Japanese management techniques (p.2).
stability, are achieved through specific functional forms. A new element is the important
role assumed by imitative activity in the ongoing global growth process. Imitative
activity diffuses leading edge technology and keeps the industry competitive in R&D.
The model is used to analyze the effects of differences in relative labor endowments on
trading patterns and technology transfer. This analysis is conducted in an integrated
global economy in which factor price equalization (FPE) prevails.
The results of the analysis can be summarized as follows. A unique, stable,
integrated equilibrium is found to exist (Proposition 3), in which both innovation and
imitation contribute to growth and welfare (Proposition 4). An increase in the world
labor endowment increases the rates of innovation, imitation, and growth: a world
subsidy to innovation (or imitation), increases the rate of innovation (or imitation)
(Proposition 5). For a large set of endowments, the integrated equilibrium can be
replicated, under factor price equalization, by trade in final goods, without direct foreign
investment (DFI) or trade in R&D services (Proposition 6). Stochastic trade patterns
with two-way international technology transfer and product cycles are generated for a
wide range of endowments (Proposition 7).
The following pages set out the model and establish the global equilibrium
(Section 3.2), examine welfare and growth (Section 3.3), discuss international technology
transfer and trade patterns (Section 3.4); and look at the conclusions to be drawn from
the analysis and elaborate implications for future research (Section 3.5).
3.2 World Economy
A representative agent maximizes utility over time and over a continuum of final
goods subject to stochastic quality increments of fixed amount. Consumer sa% ings are
channeled through an asset market to finns investing in R&D. In each industry. firms
'buy' a probability of winning the race to discover the next (or copy the latest) quality
level by engaging in costly innovative (or imitative) activity. There is free entry into
each innovation (or imitation) race. The successful innovator captures the market
through limit pricing and enjoys temporary monopoly profits until its product quality is
imitated. Successful imitators duplicate the industry leader's product quality and collude
with the quality leader to obtain temporary duopoly profits until the next innovation
occurs in that industry.
Production of final goods exhibits CRS in labor, but requires knowledge of the
current state of the art. There are instantaneous diminishing returns to aggregate industry
R&D activity. Put differently, the probability of an innovation (or imitation) occurring
is concave and increasing in the amount of resources devoted to innovative (or imitative)
activity. Unit labor requirements in each R&D activity are endogenously determined.
In the steady state, world expenditures, levels of innovative and imitative activity
per industry, and the percentage of monopoly industries are constant over time. Each
industry is first targeted for innovation, and then, for imitative, races, so market
structure fluctuates between monopoly and duopoly in stochastic cycles. The following
subsections describe consumer behavior, the product markets, R&D races, the labor
market, and the existence of the integrated equilibrium.
3.2.2 Consumer Behavior
The representative world consumer maximizes an intertemporal utility function
identical to that in Chapter 2. with a CDP instantaneous utility function. The usual static
maximization problem yields
dh, (6) E(t) (3.1)
as world industry demand at time t. where h =_ h,(w) is the highest quality available at
time t in industry w. E(t) is instantaneous expenditure, and Phi() is the price of good h
at time t
is the condition of intertemporal maximization, r(t) is the instantaneous interest rate
which clears the asset market continuously, and p is the subjective discount rate.
3.2.3 Product Markets
The current quality leader captures the market with a limit price determined by
its degree of quality advantage, which is equal to h, the quality increment over the
previous quality. If labor is the numeraire, p = X in each industry at all times. A
successful innovator becomes the sole producer in that industry and can earn monopoly
Trr E(t) i E(t) (3.3)
where (X-l) is the markup and E(t)/X is industry demand. Industries in which there is
a single producer are denoted as a-industries. When this new quality is imitated, the
winner of that race can collude with the current leader. They charge p = X, split the
market, and each earn
'c l1 2 (3.4)
I I)E(t) (3.4)
Industries with two producers are denoted as 3-industries.
3.2.4 Innovative R&D
Innovative R&D activity occurs only in duopoly, 0. industries in which diffusion
of the current state-of-the-art technology through imitation is complete.5 By engaging in
i units of innovative activity in industry o. a firm buys the probability idt of successfully
carrying out the next innovation in the industry in interval dt. The arrival rate of
innovations is a Poisson process, and the time duration of each innovation race is
exponentially distributed. Aggregate industry innovative activity, I. is the mean rate of
occurrence of innovations. Idt is the probability that if the innovation hasn't occurred
by time t, it will by time t+dt.
The firm's level of innovative activity can be related to the amount of labor it
(a, f bL, )
The variable 1, is the amount of labor hired by a firm engaged in innovation; L, is
aggregate industry employment in innovation; a, is the minimum unit labor costs of
innovative R&D. The variable b, measures the degree to which the level of industry
innovative activity lowers the individual firm's labor productivity.
5It is assumed that the whole industry (not just the monopolist) must be on the
technology frontier before it can engage in innovation. This is discussed in more detail
Aggregate innovative activity in each industry targeted for innovation is given by
The aggregate industry probability of success is a concave function of industry labor
employed in innovation. A possible source of instantaneous diminishing returns to
innovative R&D is a negative externality associated with rising industry innovative
activity. The increased possibility of parallel research programs reduces the
effectiveness of additional R&D activity in quickening the pace of innovation.6
Substituting from (3.5) for L,, unit labor requirements (and unit costs when w= 1) for
III aI b ,iLI (3.6)
I ( b11)
Innovative activity is subject to diminishing returns at the industry level, but individual
firms regard costs as constant since they take L, and I as given.
3.2.5 Imitative R&D
Imitative activity plays an important implicit role in this model. Through an
exogenous effect occurring at the end of each R&D race. the imitation process lowers
the minimum unit costs of engaging in the next innovation race. This may occur because
of experience gained in conducting R&D. Imitative activity is modeled in a parallel
'Stokey (1992) makes this same argument for instantaneous diminishing returns to
71t is assumed that these effects are large enough that innovation never occurs in an
a-industry. In monopoly, a, industries, minimum unit labor costs are assumed to be aD,,
where aID > a,. We can assume that aD -C oo. Since this is a model which considers
large innovations, as is pointed out below, this is like saying that at the time of the
introduction of black and white TV, color was not an immediate possibility.
fashion to innovative activity. By engaging in c units of imitative activity in an industry
targeted for imitation, a firm buys the probability cdt of successfully copying the current
state-of-the-art quality in that industry in interval dt. The arrival rate of imitations is a
Poisson process and the time duration of each imitation race is exponentially distributed.
Aggregate industry imitative activity, C, is the mean rate of occurrence of imitations.
Cdt is the probability that the imitation occurs in interval dt.
Aggregate imitative activity in each industry targeted for imitation is
C c (3.7)
The term Lc is aggregate industry employment in imitation: ac is the minimum unit labor
costs of imitative R&D; be measures the degree to which the level of industry imitative
activity lowers the individual firm's labor productivity. The aggregate industry
probability of success is a concave function of industry labor employed in imitation. The
source of diminishing returns to imitative R&D is also a negative externality associated
with rising industry imitative activity. Substituting from (3.7) for LC., unit labor
requirements (and unit costs when w= 1) for imitation are
uc ac ( bcLC (3.8)
C (I bcC)
Imitative activity is subject to diminishing returns at the industry level, but individual
finns view unit costs as constant by taking L, and C as given.
3.2.6 Labor Market
The competitive labor market clears at all times. The full-employment condition
L tiU1(t)l tcua(t)C (3.9)
The term L is the total world endowment of labor; E/X is the labor required to produce
final goods; u, and uc are the labor requirements in innovation and imitation respectively,
as defined in (3.6) and (3.8). The term 3 is the proportion of industries undergoing
innovation, and I is the per industry level of innovation. Hence, 0I is world innovative
activity. Also, because a is the proportion of industries undergoing imitation, and C is
the per industry level of imitative activity. aC is world imitative activity.
3.2.7 Industrial Targeting
The evolution of industries with one quality leader is
&(t) = (1 -ca(t))[l ((t)C (3.10)
When d(t) 0, as it does in the steady state,
a = 3 (3.11)
These equations are identical to (2.12) and (2.13), in section 188.8.131.52.
3.2.8 Steady-State Equilibrium
The steady state is assumed to be one in which world consumer expenditure
flows. E, and the proportion of industries with one quality leader, a, are constant over
time, and I (or C) is constant across all f (or a) industries and time. Under these
assumptions, a symmetric Nash equilibrium steady state exists with the following
characteristics: the instantaneous interest rate equals the subjective discount rate (r(t)
= p). No R&D is conducted by current monopolists or duopolists. Only duopoly
(/) industries are targeted for innovation races, and only monopoly (a) industries are
targeted for imitation. Thus, I (or C) is zero in all a (or 3) industries. There are only
two types of market structure--monopoly and duopoly. This is because, due to parameter
restrictions made for ease of analysis, collusion is only supportable between the innovator
and one imitator. There is one winner of any given imitation race. Each industry
follows a stochastic sequence of alternating periods of innovation followed by imitation.
as it climbs up its quality ladder.
There are two types of intraindustry intertemporal R&D spillovers in the steady
state. There are endogenous spillovers from innovation to imitation. In equilibrium, unit
costs of imitation are lower than unit costs of innovation. The same probability of
success in interval dt can be purchased for less in an imitation race. This type of
spillover can arise when innovators cannot appropriate all of the knowledge associated
with their product. Some knowledge may be embodied in the product, for example.
The second (exogenous) type of intertemporal R&D spillover, from one product
cycle to the next, is captured by the assumption that the minimum unit costs of
innovation, a,, are constant over time, even though each innovation is more valuable than
the previous one. In models with innovation only. this characteristic of the model is
explained as the result of exogenous spillovers of knowledge, whereby current
competitors in an innovation race can effortlessly acquire all information pertinent to the
previous innovation, which assists their efforts in the current race. This interpretation
doesn't make sense, however, in a model in which an industry makes imitative R&D
expenditures expressly to learn current technology.
In fact. though still exogenous, these spillovers can be interpreted as working
through the imitation process. The imitation process diffuses the current state-of-the-art
throughout the industry, and increases industry experience in R&D. If the second effect
is large, as is assumed, even the industry leader will not engage in innovative activity
prior to imitation. So, it may be that there are spillovers of knowledge from previous
innovations, but these are not completely disembodied. They are associated with
imitative R&D activity and can be interpreted as a by-product of the competitive race for
collusive profits. Assume that the industry in general moves close enough to the
technology frontier and gains enough R&D experience, as a consequence of the imitation
race, to engage in the next innovation race at minimum unit costs a,. By assumption, the
costs of carrying out the next innovation are prohibitively high until after imitation of the
current quality has occurred and the information obtained has substantially increased the
productivity of labor engaged in the next innovation race.
Let aID denote the minimum unit costs (labor requirements) of innovation in an
a-industry. The assumption is that
3(, a )L
aID >3( Assumption A4
Assumption A4 states that unit labor requirements for innovation in an a-industry are so
high, relative to the world endowment of labor, that innovative activity never occurs in
an a-industry. The unit costs of the innovation race to discover the j + 1h quality are aD
during the monopoly stage of quality j, but fall to a, as a result of experience gained in
R&D activity associated with the duplication of quality j. These effects are exogenous
and symmetric across industries. This characteristic leads to the cyclical nature of the
market structure in which, in each industry, each innovation must be imitated before
research can begin to discovery its replacement.
Under free entry, zero-profit conditions (ZPC), which govern the level of
innovation and imitation, equate expected discounted rewards to expected costs. The
ZPC's in each industry are, for innovation.
7I"L C vC a,
v,- u (3.12)
p 4 C 1 -blI
and for imitation,
vc = uc a. (3.13)
(pl) 1 b C
Part of v,, the expected discounted reward to innovation, are dominant profit flows, rL.
The other part of v, represents the expected value of collusive profit flows. Expected
discounted benefits to imitation, vt, are collusive profits discounted by the instantaneous
interest rate, r(t) = p, plus the probability of subsequent innovation in that industry. I.
which represents the probability that the flow of profits will stop. v, also represents
expected discounted benefits to the innovator after imitation occurs. Since C is the mean
rate of occurrence of imitations, Cv, is the expected value of collusive profit flows to the
innovator. All benefit streams to the innovator are discounted by the subjective discount
rate and the threat of imitation. By no arbitrage conditions in the asset market, v, and
vc are also the finn values of successful innovators and imitators. '
The model can be reduced to the endo2enous determination of I' and C' (*
denotes a steady state alue). How these change over time. out of the steady state.
determine how E(t) and a(t) evolve over time. In the steady state. I. C. E and a are
constant. Assume that
I T'(v, u,) (3.14)
'See Dinopoulos (1994).
C P (vc uc) (3.15)
where V' and c' are greater than zero and 'I(O) = D(0) = 0 (looking at (3.13), it is
apparent that I = 0 and C = 0 imply = 0 ). Substituting into (3.14) from (3.3),
(3.4), (3.6), (3.8), (3.9), (3.11), (3.12), and (3.13): and letting I = 0. as in the steady
(-1) IC a ac (P'I)(p C)a,
L ( c (3.16)
2 I+C 1 -bl I bcC (2(p I) C)( -bl) )1)
Substituting into (3.15) from (3.4), (3.6), (3.8), (3.9), (3.11), and (3.13); and letting
(I -1) IC a, ac ( ac
L + (p1l) (3.17)
SIC bl I bcC It bcC
Finally, combining (3.3), (3.4), (3.12), and (3.13) gives a steady-state zero-profit
at 2(p1) +C ac
(l-blI) (p+C) (1 -bC)
Note that, using (3.6) and (3.8), u,,uc is always greater than one in the steady state by
(3.18). So, there are spillovers from innovation to imitation, the magnitude of which are
endogenously determined. These R&D spillovers must exist for imitation to be profitable
relative to innovation since gross returns to innovation are greater.
Equations (3.16), (3.17) and (3.18) can be graphed as in Figure 3.1 where I, <
Io and C, > Co if
2ap > (. I)L > max iap 1 Assumption A5
a, /ac 2, Assumption A6
b > max a I and bc> Assumption A7
/' ---- C=0
0 I 1
Assumption A5 requires that the world labor force be large enough to support innovation
but not too large. Assumption A6 is consistent with innovation being more expensive
than imitation. Assumption A7 gives the stability conditions which guarantee that =
0 cuts C = 0 from above. Given Assumptions Al A7.
The Nash equilibrium steady state represented in Figure 3.1 exists and is unique
Proof: See Appendix D for the properties of (3.16). (3.17), and (3.18), which, when
graphed in Figure 3.1, shows F to be a unique equilibrium. F is shown to be a stable
equilibrium in Appendix E.
3.3 Welfare and Comparative Statics
Appendix G shows that the world representative agent enjoys a certain and
continuous growth rate in steady-state expected utility of
I 'C 'In0 1\
"g I In (3.19)
1l+C (1/1) (/C)
and steady-state expected discounted welfare of
U In -1 l (3.20)
P X I P
Both innovation and imitation influence growth, and both growth and current
expenditures affect welfare. Equation 3.20 is not surprising in a dynamic model.
Equation 3.19, however, is unusual in that imitation contributes positively to growth for
a given level of I, as is clear from the discussion of Assumption A4. Each quality level
must go through a period of innovation followed by imitation. In equation (3.19), 1/I
and 1iC are the expected durations of innovation and imitation races respectively. I/I
+ 1/C is, therefore, the expected duration of R&D activity associated with each quality
level which must occur before the next cycle can begin.
Appendix G shows that, given Assumption A4 and
b, = 2b Assumption A8
the following is true:
The t elfare maximizing levels of innovation and imitation are positive.
Assumption A8 is probably more restrictive than necessary, but simplifies the
algebra. Nethertheless, it captures the notion that innovation is more difficult than
imitation. Proposition 4 occurs because diffusion through imitation is a necessary part
of the ongoing growth. This is an interesting result because it embodies a positive role
for imitation that operates through the production side. Any positive effects of imitation
are usually thought to occur because of either product differentiation or increased
Before leaving the discussion of growth and welfare, and as a prelude to the
discussion of trade patterns, it is useful to note the effect of an increase in the size of the
economy on the rate of growth and welfare. An increase in L shifts both curves out
in Figure 3.1 but leaves Czpc unchanged (see (3.16), (3.17) and (3.18)). Therefore. I*
and C* increase, which increases the growth rate for a given level of expenditure. World
welfare rises. This demonstrates the economies of scale characteristic of these models
when R&D expenditures are spread over larger markets. The potential for gains from
integration exists. The comparative static results of subsidies to innovation and imitation
are also given in Proposition 5:
(i) An increase in the world labor endowment increases innovative activity, imitative
activity, growth and welfare.
"See Dinopoulos (1992) and Davidson and Segerstrom (1994) for examples of these
two effects. There is a substantial partial equilibrium literature that studies the
contribution of imitation to diffusion of technology. See Baldwin and Scott (1987) for
a survey of this literature and Cohen and Levinthal (1989) for a general equilibrium
treatment of this effect.
(ii) An increase in a per unit subsidy to innovative activity increases innovative activity.
(iii) An increase in a per unit subsidy to imitative activity increases imitative activity.
Proof: (i) is discussed above. (ii) and (iii) are discussed in Appendix F.
3.4 Trade and Technology Transfer
The technique used to analyze trade patterns is the integrated equilibrium
approach employed by Helpman and Knigman (1993). The integrated equilibrium.
established in Proposition I and indicated by F in Figure 3.1. represents the world
allocation of resources when labor is perfectly mobile. This section analyzes trade
patterns that can occur when free trade, between two countries with immobile labor.
replicates the integrated equilibrium and the wage rate is equalized. International
technology transfer, through imitation, influences these trade patterns. The extent of
these technology transfers is governed by relative national labor endowments. The first
subsection explores the assumptions that shape the trading environment and derives the
labor constraints for each country and the trade balance. The next subsection looks at
the conditions under which the wage rate is equal across countries. Finally, the trade and
technology transfer patterns that can occur in the replicated integrated equilibrium are
3.4.1 Assumptions/Trading Framework
The following Assumptions are made: A9 Technology cannot be transferred
costlessly between firms or across borders. A10 Labor is not internationally mobile.
All Financial capital is internationally mobile. A12 Each country targets all a (or 3)
industries equally for imitation (or innovation). A13 Each country's share of assets
equals its share of world labor. A14 The percentage of monopoly and duopoly
industries in each country is constant over time in the steady state. A15 Each country's
expenditures are constant across time in the steady state. A16 R&D and final goods
production technologies are identical across countries as is the magnitude of quality
increments. A17 Trade is frictionless and unimpeded. A18 Each country's
representative agent has the same homothetic CDP utility.
Assumption A9 is consistent with the evidence. O DFI occurs when foreign firms
conduct either innovative or imitative R&D in the home country or when home fimns
conduct R&D in foreign countries, but only imitative R&D represents the costly transfer
of technology. Since R&D technologies are identical across countries and market share
and profits are independent of both country of production and country of ownership.
there is no motive for DFI when the wage rate is equalized. Thus. it is assumed that
there are no multinationals. Licensing, one firm selling the rights of production to
another, is possible but would involve some learning expenditures of uncertain length and
effectiveness. Licensing is, therefore, compatible with costly imitation. but is not
considered. Trade in R&D services is assumed not to occur, either through DFI or
licensing. Furthermore, there are no (intermediate or capital) traded goods that might
u"See Baldwin and Scott (1987), Ch. 4. which surveys the theoretical literature and
empirical evidence on the diffusion of innovations. A general conclusion is that "the
transfer of technical information is rarely, if ever. costless: and it may be risky as well"
embody technology. Therefore, each country must invest its own resources in and win
R&D races to participate in final goods production.
The labor constraints can now be constructed. Let subscripts H and F denote
Home and Foreign variables. Let a denote Home's proportion of the labor endowment.
LH 1 L (3.21)
Define CH as the proportion of dominant firms in Home, 3H as the proportion of
duopolies based totally in Home, and 3 as the proportion of duopolies in which one
duopolist resides in each country. Let s be the fraction of final goods manufactured in
s = aH 3H 3/2 (3.22)
The Home and Foreign labor constraints are, considering Assumption A12 and using
LH /3LIH LCH (3.23)
LF (1-s)- ,3LIF aLF (3.24)
where L4H + LF = L, is total labor employed in innovation, and LCH + LpC = L, is
total labor employed in imitation.
Consider Home's share of manufacturing. Assumptions A12 and A14 imply that
aH 3IHdt aH Cdt 0 This, together with (3.11), implies that
aH H (3.25)
The same assumptions imply that f"H aCH H H 1H I 0 or
C l o
/H CH IH (3.26)
Since / /H / F = 0 it follows that / aCH H+ OHCF 3I' 0 or
F p- aH (3.27)
All this implies that
H 2/2 H,-C' 0 (3.28)
These equations are easily interpreted. Recall that there is no trade in R&D services so
that all production within a country is due to R&D carried out in that country. Then s
and (1-s) are determined by the relative amounts of R&D done in each country. For
example, if Home does one half of the world innovative R&D. by the Law of Large
Numbers, it will win one half of innovation races and, in the steady state, will have one
half of all dominant firms. If Home also does one half of all world imitative R&D. it
will have one half of all duopoly industry firms. Home would then have one half of all
Turn next to the trade balance. Since each consumer is completely diversified,
each will own a share of each successful firm in the exact proportion to her share of
world assets. Given international financial capital mobility, consumer intertemporal
maximization, and EH EF E 0 then, r = rH = r = p in the steady state. Let
Y = YH + YF be the total value of world assets, in the steady state, made up of assets
held by the Home and Foreign agents respectively. Let VH be the total value of Home
VH H V H I (13 /2)Vc
Then, Y = V = VH + VF = av, + i3vc. Y must be constant by Assumption A15.
Since E. I, and C are constant, v, and v, are also constant (See (3.3), (3.4), (3.12),
(3.13)). Since & 6H = 0 by Assumption A14, VH and VF are constant. Note
that, by Assumption A13, Home's share of world assets is equal to its share of labor.
Then. YH = aY = aVH + oVF and Y, = (1-U)VH + (1-o)VF. Since there is no trade
in assets, the current account must balance:
s- (1-s)- pVF (1 O)pVH 0 (3.30)
The first term is Home exports: the second is Home imports. Their difference represents
the merchandise trade balance. The third term. Home's interest receipts, less the last
term. Home's interest payments, is the service account.
3.4.2 Factor Price Equalization Set
The FPE set, or set of relative national labor endowments which can reproduce
the integrated equilibrium, can now be derived. In this model, FPE will always hold if
both countries engage in R&D activity. Because of integration of final goods markets
(which implies a single global innovation race with a single winner) and the nature of the
externality associated with R&D activity, world labor employed in innovation (or
imitation) determines firm and industry unit labor requirements at home and abroad."
Unit labor requirements are endogenous, but are always equal across countries in each
"If a different, country-specific, source of instantaneous diminishing returns to R&D
(such as immobile specific factors) is assumed, then a wage differential can occur which,
if large enough, will lead to a collapse of the collusive equilibrium. The model would
then revert to a North-South model.
R&D activity, and also in final goods production, by Assumption A16. Countries cannot
specialize in production, however, without incurring R&D expenses, by Assumption A9.
Because specialization is impossible, the wages in each country must be equal.
Suppose that the wage in Home. wH, is higher than the wage in Foreign. WF. Unit costs
of both R&D activities will be greater at Home (u,'WH > u,'WF ,. ucWH > uCwWF).-
Similarly, since marginal costs of final goods production are higher at Home (wH > WF),
profits and expected discounted benefits to either R&D activity will be lower at Home.
By financial capital mobility, funds would flow to Foreign R&D races, bidding up wages
there and lowering wages at Home. Labor mobility within each country, and trade and
financial capital mobility between countries. equalizes wages. Consequently, as long as
each country has a sufficient relative endowment of labor to acquire production through
innovative R&D at u,', imitative R&D at uc'. or both, the integrated equilibrium can be
reproduced by trade under FPE.
Defining the FPE set is a matter of determining what the minimum share of labor
is for each country to men.age in R&D and the associated production. Because each
country is assumed to engage in innovation in all 3 industries, and imitation in all a
industries, and because each country must engage in production of final goods for every
race it wins, there is a minimum labor endowment below which the country cannot carry
out these activities. For any endowment point that allocates a share of labor less than
2u1* and ut' are the global integrated equilibrium steady state unit labor requirements
in innovation and imitation respectively.
this minimum to either country, the integrated equilibrium will not be reproduced by
trade under FPE.
The FPE set is represented graphically in Figure 3.2. Let the total length of the
line be L. The Home country's share of labor increases as the endowment point moves
to the right. The Foreign country's share increases as it moves to the left. The point
labelled L, represents the endowment point for which Home's share of labor is at the
minimum necessary to sustain production through innovation or imitation, whichever
requires less labor at the margin in the integrated equilibrium. The point labelled LF
-0 FPE L- -
--------- FPE -----------
LH LMM F LFM
Factor Price Equalization Set
represents the same for the Foreign country. Hence, in the regions 0 LH and
L, L FPE cannot be maintained by trade under the assumptions outlined above.
In the first region, Home is too small: in the second. Foreign is too small. 3 Therefore,
LH LF is the set of endowment points for which both countries are large enough
to conduct R&D at u,* and uc, and carry out the associated production. FPE must occur
through trade, and the integrated equilibrium will be reproduced. The results of this
section are summarized in Proposition 6:
If the distribution of labor endowments lies in the region L, L, in Figure
3.2. the integrated equilibrium. represented by F in Figure 3. 1, can be achieved by
balanced trade, between similar countries, in which there is no DFI or trade in R&D
3.4.3 Trade Patterns
Having defined the FPE set, it is now convenient to turn to the characterization
of trade patterns that can occur when the endowment point is in the FPE set. It is
possible to get an expression relating Home's endowment of labor to Home's labor
allocations across activities in a way consistent with the allocations in the integrated
equilibrium. Assume that L the total world endowment of labor, satisfies Assumption
A6, and the endowment point is in the FPE set. Relaxing the normalization on labor so
"These minimum endowment points are derived in the Appendix H. It should be
noted that, because each industry is of measure zero, if Assumption A13 is relaxed so
that a country can target a selected set of industries for R&D, FPE will occur for all
possible endowments. However, almost any alternative to Assumption A13 will render
the model either more complicated or less interesting. A relaxation of Assumption A0.,
so that multinationals can costlessly transfer production abroad, will also assure FPE for
all possible endowment points, but that would be contrary to the evidence. Neither of
these points will be pursued further because trade patterns are only analyzed within the
that demand for labor in Home production is per industry; using (3.3), (3.4),
(3.12) and (3.13) in (3.23) and (3.24); solving for wH and wF; and setting them equal
gives, after some manipulation,
(sL LH) (s-o)L /3(sLI LIH) Y'(sLc LCH) (3.31)
This equation summarizes the patterns of labor employment at Home that are consistent
with FPE. If the world economy can be represented by an integrated equilibrium in
which each country faces the same prices and techniques of production, this equation
must be satisfied. The special case. discussed below, will make it clear that this set is
not empty. From (3.31) alone, under factor price equalization, there are multiple
possible allocations of labor across activities in each country. Therefore, the pattern of
trade is indeterminant.
Nethertheless, additional assumptions will uncover the rich patterns of trade
possible in this model. Refer back to Figure 3.2. LH is defined as the minimum
labor endowment point below which the home country is too small to conduct both
innovation and imitation, and the associated production of final goods. LF is
defined in a similar fashion for the Foreign country. If the endowment point falls within
-MM M I MNI
LH L both countries can engage in both types of R&D activity and the
associated production of final goods.
MM M Al s
Assume that the endowment point is in the region LH L Also assume
symmetric labor activity. The two countries employ labor in each activity equal, in
proportion, to their relative labor supply. Then. LIH = aL, and LCH = uLc, which
implies that IH = al and CH = oC. So, from (3.25), XH = ooe: from (3.28).
(WH //2) a o3; and from (3.22), s = o: so that sL, = LI and sLc = LCH. Refer to
Figure 3.3 for a graphical representation. The top parallel line represents the allocation
of labor to final goods production, Lp* = E/X, innovative activity, L,'. and
0 L Le L
0 R E
LPH LH LCH
imitative activity. Lc', in the integrated equilibrium. The bottom parallel line represents
the set of endowment points. OH is Home's origin; OF is Foreign's origin. For any
endowment point. E, OHE is Home's endowment of labor, and EOF is Foreign's
endowment. A diagonal line is drawn from OH to L and from E to L. Dropping
perpendicular lines from K and J to diagonal OHL forms similar triangles GJL. DKL and
OHOL. which makes GL/OHL = JL/OL, DG/OHL= KJ/OL, and OHD/OHL = OK/OL.
Similar triangles OHLE, OHGR, and OHDQ are formed by dropping lines parallel to LE
from D and G to OHOp. LPH, LIH and LCH are the allocations of labor to final goods
production, innovative activity and imitative activity respectively. By the properties of
similar triangles. LPH/Lp* = LIH/L`* = LCH/Lc' = OHE/OL = o. A similar diagram can
be constructed for the foreign country.
In addition to lending itself to convenient graphical representation, this symmetric
case also simplifies the trade balance. With EH 0 and w = 1,
EH LH + CpY a- L p Y (3.32)
is expenditure at home. Also, VH = oav, + avc = aV. and the service account must
balance (see equation 3.29). The shares of Home and Foreign expenditures. assets, labor
in imitative and innovative activities and in manufacturing are equal to their shares in
labor. So a and (1 s) (1 r) Equation 3.30 becomes
EF EH E E
s- (I -s) o'(l ao) (1 O)a-- (3.33)
The merchandise trade account must balance if Home's proportion of manufacturing is
equal to its proportion of assets. which is equal to its proportion of labor.
In this symmetric integrated equilibrium, Home will export from cH,, H (and 3
industries if E, < EF or o < V). It will import from aF and 3F industries. Thus, this
model generates product cycles among different sized countries. For example, suppose
that an industry is dominated by a Home monopolist so that Home initially exports from
this industry. Suppose that a Foreign firm successfully imitates this monopolist's quality.
The Home and Foreign firms split the world market. If a is greater than one half. Home
will now import in this industry. Another industry may not experience product cycles.
A Home monopolist may be imitated by a domestic firm so that Home continues to
dominate and export from this industry. In still another industry, say a duopoly based
wholly at Home, a Foreign firm may capture the entire market share through innovation.
Consequently, Home may go from exporting to importing in that industry and may also
recapture some of the market through imitation.
In general, Home and Foreign market shares fluctuate across industries. aHCFdt
Home monopolists lose half their market shares to Foreign imitators in dt, and acCHdt
Foreign monopolists lose half their market shares to Home imitators. Also.
2(fH //2)lFdt Home duopolists lose their total market shares to Foreign innovators.
and 2(3F -1 /2)IHdt Foreign duopolists lose their total market shares to Home
innovators. The pattern of trade fluctuates and has richer possibilities than a model of
endogenous innovation alone. In particular, it is possible, in this model, for a country
to capture part or all of the market in some industry and lose part or all of the market
in other industries during the same period.
In each interval, dt. Foreign imitators successfully transfer technology from
c.HCFdt = ((l-a)a'C'dt Home monopolists, and Home successfully transfers technology
from Foreign monopolists in acCHdt = (l-a)oa'C*dt industries. In the symmetric case.
these transfers are equal. Let 4H ( F ) be the proportion of duopoly industries in which
Home (or Foreign) has successfully transferred technology from a Foreign (or Home)
at fCH 3I' ^ (la)af3- (1 u)a (3.34)
A similar calculation gives 3pF (1 a) /3' and H /3 OF The transfer of
technology from Home to Foreign (and vice versa), and the associated transfer of market
share, are related to the global intensities of imitative and innovative activity. For given
levels of I* and C*, the endowments of labor endogenously determine the extent of
technology transfer. a = /2 maximizes these transfers. Intuitively, the more equally
endowed the two countries, the more they interact.
The pattern of trade, under the assumption of symmetry, fluctuates stochastically,
involves two- \way endogenous international technology transfer and product cycles (when
a # V), as well as intranational endogenous technology transfer. The extent of both
technology transfer and product cycles is determined by the intensities of global
innovative and imitative activities and relative national labor endowments.
This paper constructs a Neo-Schumpeterian model of growth and trade between
advanced countries. The model emphasizes the roles of costly and risky innovation and
imitation, and incorporates instantaneous diminishing returns to each R&D activity.
There is industrial targeting for R&D in which industries undergo cycles of innovation
followed by imitation. Spillovers from innovation to imitation occur because unit costs
of imitation are lower than those for innovation. Spillovers from imitation to innovation
occur because R&D experience gained from imitative R&D activity lowers the costs of
subsequent innovation. In this model, the integrated equilibrium can be achieved by free
trade, with no DFI and no trade in R&D services.
The results of this model can be compared to previous work. In contrast to
Grossman and Helpman (1991a), trade occurs under FPE. and innovation and imitation
can occur in both countries. This allows the possibility of richer patterns of trade.
These patterns of trade are similar to those in Dinopoulos et al. (1993), but there is no
costless transfer of technology, a characterization consistent with the Industrial
Organization literature on diffusion. In particular, the present model allows for
technology transfer in both directions and for countries to capture part of the market in
some industries, instead of the entire market.
INTERNATIONAL R&D KNOWLEDGE SPILLOVERS
[A]cademic and policy discussions...might be more fruitful
if we spent less time working out solutions to systems of
equations and more time defining precisely what the words
we use mean.
Neo-Schumpeterian growth literature may not hinge on the existence of sizeable
R&D knowledge spillovers, but they make the theorist's life easier. Consequently,
empirical investigation into the nature, magnitude, and extent of spillovers of knowledge
from R&D activity currently attracts a lot of attention. Detection of R&D spillovers is
also important for accurate measurement of the social returns to R&D--critical for
optimal R&D policy discussions. Nowhere, however, is the possible presence of
spillovers more interesting than in the interactions among countries. It matters for
foreign investment policy, national industrial policy, and international intellectual
property rights protection. The new growth theory further suggests that strategies that
increase the flow of spillovers will accelerate growth. Thus, it presents the enticing
possibilities of rapid economic development for some less developed countries and
increased efficiency for fully integrated economies.
Unfortunately, these spillovers are extraordinarily difficult to identify and
measure, despite numerous efforts to do so. Part of the problem is that theoreticians
generally use exogenous spillover effects as a tool in their models rather than focus on
theoretical examination of the forces that influence or are influenced by these spillovers.
Additionally, because of the host of observability and definitional problems surrounding
the concept of international R&D knowledge spillovers, empirical work is problematic.
The theoretical and empirical importance of these spillovers was touched on in section
1.4 of Chapter 1. The current chapter is meant to address the question: what are
spillovers and how do we measure them? The focus is on international, intraindustry
R&D knowledge spillovers.
The main thrust of this chapter is to dispel the prevalent notion that spillovers are
an unlocked for and costless boon to recipients; that, once acquired by one agent, the
marginal cost of knowledge to other agents is close to zero. Just sitting in the physics
section of the library does not make one a physicist. The prospective scientist must
invest time and money.' Just so, firms must invest in R&D activities to copy the
innovations of other firms in the industry. They may spend less because of information
acquired as a result of the previous success, but if they do not engage in R&D activity,
they will not enjoy any pure spillover benefits. Alternatively, firms may maintain small
'Notwithstanding the possibility that playing tapes while you sleep or sleeping on a
book may have some positive but costless effect.
investments in various auxiliary R&D programs that are designed to position the firm
so as to maximize any expected spillover benefits from possible innovations by rivals or
related industries. Studies that do not recognize these expenditures may present biased
estimates of the magnitude of spillovers.
This chapter builds on the model of the previous chapter in order to clarify the
issues involved in defining and measuring R&D knowledge spillovers. It is relatively
straightforward to define a national quality index or stock of knowledge for the model
presented in Chapter 3. An equation of knowledge accumulation can be derived and
compared with estimated equations, in the existing literature, which attempt to measure
international spillovers. I conclude from this comparison that the existing studies are
not capturing true spillover effects because they do not distinguish between innovative
and imitative R&D activity or account for other diffusion expenditures. Furthermore,
'spillover-seeking' behavior by profit maximizing firms militates against the presence
of sizeable free-rider benefits from spillovers.
Section 4.2 discusses the meaning of R&D knowledge spillovers in detail.
Section 4.3 extends the model of Chapter 3 to an operational equation of national
knowledge accumulation which is compared to existing studies. Section 4.4 discusses
issues of spillover measurement. Section 4.5 concludes.
4.2 What Are Spillovers?
Knowledge is nonrivalrous and at least partially nonexcludable, so it is no surprise
that externalities, or spillovers, are associated with its production. What muddies the
waters are the presence of more than one type of the flow commonly referred to as R&D
spillovers, and, of course, the unobservable nature of knowledge. These various flows
have different consequences for theory and policy so it is important to distinguish
between them. I use Figure 4.1 to identify these flows and the associated spillover
Innovative R&D activity results in some new or improved process or product.
Four benefit flows can be distinguished. The first stream includes all direct benefits that
the innovator captures through (temporary) market power associated with the innovation.
These flows may include profits from sales of superior products, productivity gains, and
licensing. This stream, resulting from market transactions, is perhaps the easiest to
measure. It represents the private return to R&D. When added to the three remaining
flows, the result is the social return to R&D.
The second stream is direct benefits to customers of new products or existing
products for which prices have dropped due to process innovations and competition.
Because monopoly power is imperfect, and because the innovator may not foresee all of
the uses of the new product, customers will not in general, pay the full value of the
innovation. This second flow is a pecuniary externality associated with the product. It
Innovative New Product
R&D or Process
Benefit Flows From Innovation
arises because of market imperfections, competition, and measurement errors, not
market failure. Accurate measurement of this potentially large benefit stream is
essential for the calculation of the social return to R&D. Identifiable in principle, this
flow is harder to measure than the first benefit stream. It does not represent, however,
true R&D knowledge spillovers, although often measured as such.
Griliches distinguishes between the spurious spillovers of flow 2 in Figure 4.1 and
what he calls true spillovers: "ideas borrowed by research teams of industry i from the
research results of industry j." (1992, p. S36) Of course, i can equal j, and 'industry'
can be replaced by 'firm.' Because I distinguish between innovative R&D activity and
imitative R&D activity, I further categorize these 'true' spillovers into two types
according to the type of R&D activity of the recipient:2
The third flow is knowledge transfers to current competitors, who cannot be
prevented from duplicating the new product or process at lower R&D cost. To the extent
that competitors must devote resources to this noncooperative technology transfer, this
is a measurable flow which is an externality to the innovator, not to the recipient. But,
to the extent that the costs of imitating are lower than the costs of innovating because of
the nonexcludable nature of knowledge, these are free-rider spillovers from (primarily)
innovative activity to (primarily) imitative activity.3 These are static spillover effects in
the sense that they do more to affect current market structure than future knowledge
accumulation. If innovation and imitation costs vary independently with the level of
activity, the magnitude of these spillovers is endogenous.
The last benefit flow identified in Figure 4.1, flow 4, is the benefit to future
innovators. This is the spillovers concept most often employed in the new growth
models to overcome any long-run diminishing returns to R&D. It is also the most
difficult flow to identify and measure, since it is related to the intertemporal, public-good
2The stylized model of Chapters 2 and 3 envisions major innovations followed by
exact duplication by imitators. In reality, imitators may make minor improvements to
differentiate their products or improve a process while adapting and adopting it. These
relatively minor changes could be interpreted as innovations in another model and may
sum to substantial increments in knowledge. Individually, however, these 'imitations'
will not have the same impact on knowledge production as major innovations.
3These spillovers are not just from reverse engineering or weak patent laws. The
reduction in uncertainty, arising from the simple knowledge that a particular line of
research was fruitful to a competitor, may be important, allowing the imitator to conduct
a narrower research program.
nature of knowledge. These spillovers arise because those firms engaged in current R&D
activities add to the stock of knowledge. This is a key factor in affecting future
innovation in that industry and others. But, the ways in which these spillovers actually
occur are difficult to quantify. They are of a different, more elusive, quality than the
nonexcludability spillovers of flow 3 in Figure 4.1. It is not simply a matter of it being
easier to copy than to create. It is picking up clues as to the nature of the unknown,
which illuminate the most effective path to the next stage, competitive arena or state-of-
the-art in the industry.4 How can this effect be detected, especially if internalized by
firms currently at the state-of-the-art, either through innovation or imitation, and engaged
in a race to discover the next state-of-the-art in the industry?
There is both theoretical and empirical evidence that intraindustry transfers of
this type require recipient R&D expenditures to be able to take advantage of any new
additions to the knowledge stock.5 Simultaneously engaging in similar innovative
activity may position the firm to take advantage of spillovers from a rival, but
concurrent maintenance R&D activity or subsequent imitative activity, or both, are
substitutes for innovative activity in this role (flow 5 in Figure 4.1). Further, if the
innovation is major, unsuccessful rivals may still require expenditures to copy the
successor to maintain their R&D competitiveness and market share. Familiarity with the
4Kortum (1995) suggests a search model of innovation in which successful research
spills over to subsequent research by shifting the underlying distribution of undiscovered
techniques, thus maintaining the pool of potential improvements.
5 See Cohen and Leventhal (1989), Henderson and Cockburn (1995), Nadiri (1993),
and Griliches (1992) on this point.
current state-of-the-art seems essential. So, in principle, these spillovers are also
associated with R&D activity on the receiving end and are therefore endogenous.
4.3 Acquired Knowledge or Spillovers?
In this section I use the model previously developed in Chapters 2 and 3 to
interpret current efforts to measure spillovers. Recall that, in this model, endogenous
innovative and imitative R&D contribute to long-run growth in consumer utility through
quality improvements. Both are Poisson processes with endogenous arrival rates. I =
I(L), (C C(Lc) ) is the arrival rate or intensity of innovative (or imitative) activity per
industry, L, ( Lc) is labor employed in innovative (or imitative) activity per industry ,
and I'(L,)>0, C'(Lc)>O, I"(L,)<0, C"(Lc)<0. There is free entry into each activity,
firms are atomistic, and industries are targeted first for innovation and then for imitation.
Below I reproduce the key equations of the integrated equilibrium:
v, = u1 (4.1)
vc c = uc (4.2)
(P + I)
Equations 4.1 and 4.2 are the zero-profit conditions (ZPC) for innovative and
imitative activity, respectively, in the steady state, where rL are dominant firm profits,
rc are collusive profits, p is the discount rate, and u, (or uc) is the unit cost of
innovative (or imitative) activity. Equations 4.1 and 4.2, along with a labor constraint
(not reproduced here), completely describe the integrated equilibrium steady state.
In this model, with free trade between two advanced countries (Home and
Foreign) and international capital mobility, growth in consumer utility is always equal
in the two countries. A quality index can be defined, however, for which the global
growth rate is equal to growth in consumer utility. A distinction can be made between
this growth rate and the growth rates of national quality indices. Define the global
quality index or stock of knowledge as
Atf =Jln.'A dto (4.3)
where ht(w) is the state-of-the-art quality in industry w at time t, w e [0,1], and In X is
the knowledge increment associated with each state-of-the-art product. Then, Appendix
G shows that
A =T3**lnX g' (4.4)
where g', given in (3.19), is the steady-state rate of growth of global consumer utility,
I" is the steady-state level of innovative activity or the mean rate of occurrence of
innovations, and 0* is the steady-state percentage of industries targeted for innovation,
given in (3.11). The rate at which the world quality index grows equals the proportion
of industries targeted for innovations, times the mean rate of occurrence of innovations,
times the knowledge increment of each innovation. This growth rate is always equal to
Compare this with the growth rate of Home's stock of knowledge. Home's stock
of knowledge is
AHt = fnjh" )do (4.5)
where hHt(o) represents the highest quality available in Home from domestic firms in
industry w at time t. In the steady state,
AH = (apCH + IH)1n (4.6)
where cF, is the percentage of Foreign monopolies targeted for imitation by Home firms,
CH' is the level of Home imitative activity per industry, and IH* is the level of Home
innovative activity per industry in the steady state. Home increases its stock of
knowledge from both innovation and technology transfer from abroad through imitation.
represents the rate of technology transfer from abroad through imitation.
The national growth rates of knowledge can be compared to the global rate under
the symmetric case already examined in Chapter 3. Recall that a is Home's share of the
world labor endowment, and s is its share of final goods production. In the symmetric
case, r= s, aF = (1-a)a', CH = oC', and I'H = al', so that
AH = (aC* + P'IH)lnA = (2-a)ag > ag" (4.8)
for a greater than zero. Home's stock of knowledge, and consumer utility, grow faster
than its share of innovation would imply due to the costly international transfer of
technology through imitation. So, even among advanced countries, international
technology transfer is an important element of growth.
Equation (4.6) can be compared with a class of papers attempting to measure
international spillovers of knowledge by estimating an equation of the general form
G = 6,RH + FRF + c, (4.9)
where G is growth in total factor productivity (TFP) or labor productivity, R, is some
measure of Home R&D activity such as expenditures, Rp is a measure of similar foreign
R&D activity and Ec is an error term. The parameter 5 is thought to measure spillovers
from foreign or borrowed R&D.6 This equation is meant to measure the relative
importance of Home and Foreign R&D for national productivity growth. Rewrite (4.6)
AH = XcC + XIIH + E, (4.10)
where A = In ., X, = InX, and e2 is an error term. The impact on knowledge from the
two sources is allowed to vary. An equation such as this can be estimated for the U.S.
across industries and over time (time and industry subscripts omitted).
AH is the gross increment in knowledge per period. This variable is not
directly measurable, but a reasonable proxy could be the change in industry stock market
value per period. If the degree of appropriability of the firm vis-a-vis the consumer is
relatively constant, this method might sufficiently capture the net increases in the value
or quality of the industry's products. Let AH = CS + E3 where S is the change in
stock market value in each period. If is constant across time and the variance of E3 is
6See Nadiri (1993) and Griliches (1992), for discussions of this literature.
7In principle, other technology expenditure flows, such as patent purchases and
licensing should also be considered. See Nadiri (1993) for evidence that these flows have
increased. See Kokko (1994) and Saggi (1994) for discussions of spillovers associated
small, this will be a reasonably good measure of the growth in quality or knowledge
attributable to innovation.8
There are advantages to this approach. First, directly estimating the effects of
R&D activity on firm value, not its impact on productivity, leaves aside the problem of
separating out the effects of learning-by-doing and human capital accumulation, which
do not have the observability of R&D, nor the news event characteristic of innovation.
Second, this approach is not limited to process innovations, for which only a nonconstant
portion of R&D is undertaken.9 Third, it reduces the possibility of inadvertently
capturing 'spurious' spillovers through incorrectly measured input prices (type 2 flows
in Figure 4.1); the problem of correctly deflating R&D expenditures to obtain measures
of real R&D activity is still present. Fourth, it reduces the timing problem of when
R&D affects productivity. R&D news will be immediately incorporated into stock
market values. Many studies use cumulative R&D flows to alleviate this difficulty,
8 An alternative is to use some quality adjusted patent count. See Griliches (1992)
for a discussion of the shortcomings of patent data. Patents are said to be a noisy
measure of innovative output. Some innovations aren't patented. Not all patents have
value, and their value varies over time. Current received wisdom is that regressions of
firm value on measures of R&D input perform better than such regressions with patent
counts as the dependent variable. See Thompson (1995b). There have been recent
attempts to improve our understanding of the relationship between innovation and
patents. See Eaton and Kortum (1994) for a model of technical change and diffusion
across countries in which the decision to patent is endogenized.
9Thompson (1995b) develops a model in which an innovation directly affects firm
value, thus capturing the effects of both process and product innovations. The reduced
form of his model also includes current profits as a determinant of firm value.
Alternatively, a model of process innovation equivalent to the model developed in
Chapters 2 and 3 could be used. In this case, A, is equivalent to TFP growth.
which is especially problematic because the effects of foreign R&D may have longer lags
than own R&D effects.
In equation 4.6, CH is per industry imitation activity, and aU is the percentage of
foreign monopolies targeted for imitation. Similarly, IH is the per industry innovative
activity, and 0 is the percentage of firms targeted for innovation. In practice, the
intensity of R&D activity and its impact on the stock of knowledge will vary across
industries, and innovative and imitative activity will occur simultaneously in each
industry.10 So, in (4.10), ap* = I' = 1 and Kc measures the average impact on the
national knowledge stock of primarily imitative activity directed at noncooperative
technology transfer from abroad in each industry. The impact of Home innovative
activity is 1 ."
Note that, in (4.9), RH = CHF + CHH + IH. The difference between X1 and 6H
is that 65 measures the impact of all Home R&D activity, forcing X1 = ic, and
overmeasuring, by CHH, the R&D activity directed at increasing the national knowledge
stock. By similar reasoning, 6, measures the effect of foreign R&D, RF = CF + I,,
without recognizing that CF should have little effect and without considering the costs of
bringing about these 'spillovers' (namely CHF). In contrast, RF does not enter into (4.10).
'"See Klenow (1994) for a model that explains cross industry variations in R&D
activity through variations in technological opportunity, market size, and appropriability
of innovations. See Davidson and Segerstrom (1994) for a model qualitatively similar
to that of Chapter 3 but in which innovation and imitation occur simultaneously in each
"A term could also be added that measures aggregate national imitative activity to
test the assumption, made in Chapter 3, that imitative activity may directly contribute to
the stock of knowledge, through learning-by-doing in R&D.
Much of what is considered spillovers may be costly transfers, which can be estimated
through diffusion expenditures. 5H may underestimate the effectiveness of IH, and bF
may not be accurately capturing spillover effects.
To illustrate this last point, ignore the differences between the left-hand side
(LHS) of equations (4.9) and (4.10), or assume AH = G, as in footnote 9. Suppose that
Home innovation can be related to total Home R&D, and the intensity of imitation of
Foreign innovations is positively related to the intensity of foreign innovation:
IH = aRH + e, a
and CF = bRF + e.
Substituting these into (4.10), and comparing the result to (4.9) shows that, if (4.10) is
the true model, then 5H = aXIH < X1H, SF = bc 1 Xc, and E, = E2 + ,el +4-ce2.
Note that the effectiveness of Home innovative R&D, 1H, is underestimated by 6H ,
and 6F is inaccurately capturing the effectiveness of Home imitative R&D, which may
include spillovers from Foreign R&D. Furthermore, Variance(e,) > Variance(E2).
These facts imply that equation (4.10) should improve over (4.9).
The question is, then, how to allocate expenditures between substantially
innovative activity and substantially imitative activity. If this cannot be done efficiently
and satisfactorily, then estimating equation (4.11) will not improve over (4.10). One
possibility is to allocate by size of research programs. It could be assumed that small
programs are, primarily, maintained in order to facilitate spillovers, while large programs
are innovative.12 This separates R&D activity into imitative and innovative activity, but
the proportion of imitative activity directed at foreign firms must be determined. If there
are adequate data on patent infringement complaints, then the ratio of foreign complaints
against domestic firms to total complaints against domestic firms, Z, can provide an
estimate of CH .13 Then,
^H C= CH + (4.11)
Finally, C, and I, must be converted from unobserved intensities of R&D activity
into R&D expenditures. Suppose that, instead of the specific functional forms of
Chapters 2 and 3, CH and IH take the following forms:
CH = acLCH (4.12)
and IH = aLi (4.13)
Since the primary purpose is not to measure diminishing returns to R&D, assume that
0 = 4, for which estimates are provided for 16 industry groups by Thompson (1995b).
Substituting for these in (4.12) and (4.13), and using (4.11), allows (4.10) to be rewritten
S = YILH + Y2LI + 5 ,(4.14)
'2This could be expensive and time-consuming, of course, requiring a high degree
of disaggregation, but this regression could be done for a single industry. Henderson and
Cockburn (1995), for example, have collected such data for the pharmaceutical industry.
"Alternatively, since imitators must often license some key component, licensing data
may be useful.
E2 E3 E4
LeH and Lm can be interpreted as innovative and imitative R&D expenditures,
respectively. These are allocated, as discussed above, by research program size, and
may be measured with error, but E(E5) is still zero. The variable is constructed from
patent infringement data, licensing data, or other data that might be used to distinguish
between imitative activities directed at Home and Foreign firms.
From examination of (4.14) and (4.15), distinguishing between these R&D flows
is important. Notice that even if Xc = X1, 0 = 0, and a, = ac, then y, yz, because
only a fraction of imitative activity is directed at foreign firms. y, and 72 measure the
impact on the quality or knowledge index of imitative activity that transfers technology
from abroad and innovative activity that creates knowledge at home. If Xc = X,, as
implied by the model, and 0 = 4, then yi / > 72 implies that ac > a,. In what sense,
then, can this be called a measure of the magnitude of spillovers from innovators to
imitators? This is the topic of the next section.
4.4 Measuring Spillovers
For the model used here, type 4 spillovers in Figure 4.1 are exogenous. Type 3
spillovers, however, those from innovators to imitators are endogenous, at least in the
sense to be explained below. If ac in (4.12) is greater than a, in (4.13), and 0 = 4), the
same level of effort gives a higher probability of successful imitation than innovation.
If the only factor of R&D production is labor, which is the num6raire, (4.12) and (4.13)
imply unit costs of
1 1/e 0 -
uc -= C = a cCo (4.16)
uI = aI' (4.17)
SI = -- (4.18)
SMF = u (4.19)
be defined as the magnitude of intraindustry spillovers from innovators to current
competitors at the industry and firm levels respectively. Equation 4.18 is exogenous,
presumably determined by such effects as industry specific appropriability characteristics
and information technology. In (4.19), unit costs are determined in equilibrium (as
indicated by *) at the industry level, by, among other things, L the world labor
endowment. S, could also be affected by intellectual property rights protection,
subsidies and firms' expectations about future profits.
If firms are atomistic, then they take (4.19) as given. If SM < 1, then there are
exogenous spillovers at the firm level as well. But,
SM, = (4.20)
and vc* < v,*, by construction, in this model. Since the successful imitator splits the
market with the innovator, the expected discounted benefits to imitation cannot exceed
the expected discounted benefits to innovation. Of course, this need not be generally
In any case, S, # S. except by coincidence (or if unit costs are constant, which
is not borne out by the substantial empirical evidence of instantaneous diminishing returns
to R&D)14. So, if the regression described in section 4.3 is carried out and an estimate
of SM is obtained, it must be interpreted as occurring at the industry level. Firm level
type 3 R&D spillovers from innovative activity to imitative activity, SM, may be larger
or smaller than those which occur at the industry level." Which measure of spillovers
to use matters depends on the context. S. is independent of policy; Sm is not.
'4See Griliches (1992), Nadiri (1993), Thompson (1995b), and Henderson and
Cockburn (1995) for evidence of instantaneous diminishing returns to R&D.
"This discussion assumes, as in Chapter 2 and 3, that u,' and c' are determined
independently and at the industry level. How realistic this assumption is depends on
industry specific characteristics. It may take specific skills to run smaller programs
designed to duplicate another's success as cheaply as possible, as compared to running
large innovative projects. If these specific skills are in fixed supply and firms are small
and competitive, then these costs will be independent.
The magnitude of spillovers from innovators to imitators is important for the
discussion of North-South trade. There are many models that imply that imitation coupled
with production cost advantages is an effective course of economic development. 6 The
larger the magnitude of spillovers, the more effective this course of development. A key
issue is the possible existence of a geographic dimension to spillovers. In
(4.18), ac may be a function of distance from the innovating firm or country because,
say, spillovers work partially through the labor markets. This is a natural barrier to
foreign competition, which may be counteracted by the foreign government through
policies which affect S,. These may include designing intellectual property rights
protection laws that favor imitators or subsidizing imitation.
This type of spillover also matters for national patent law and optimal R&D
policy. In welfare considerations, the benefits of imitation are usually considered to be
lower prices and increased variety. These are balanced against the incentives to
innovate. A complicating factor is the existence of the innovation to innovation
spillovers of type 5 in Figure 4.1. To the extent that imitators can expect spillovers to
their own innovative activity and incorporate these expectations in vc, they will increase
their imitative activity. This imitation may be the most efficient means of staying
competitive in R&D, and this consideration must also be balanced against the incentives
to current innovators.
'6See, for example, Grossman and Helpman (1991a) and Barro and Sala-I-Martin
(1995), Ch 8.
Although this chapter does not model spillovers from innovation to innovation of
type 4 in Figure 4.1, it does offer some observations. A dominant theme of the chapter
has been the necessity of engaging R&D activity in order to benefit from spillovers. Just
as imitators may incorporate anticipated spillovers into expected benefits, vc, innovators
will incorporate them into v,. Cohen and Levinthal build a model in which "absorptive
capacity represents an important part of a firm's ability to create new knowledge," and
in which "spillovers may encourage [innovative] R&D under some conditions." (1989,
pp. 570, 574)
This 'spillover-seeking' behavior by innovators complicates the discussion of
optimal R&D policy further. Increasing the ease of dissemination of knowledge may
increase innovation. Moreover, these increased expenditures may lower the magnitude
or value of anticipated spillovers. For type 3 spillovers, in Figure 4.1, if vc is large
relative to v1, firm level spillovers will be small, even if industry level spillovers are
large. If the magnitude of type 4 spillovers per innovation does not increase with the
level of innovative activity ( v, does not increase with I) the same effect can occur
Evidence that firms engage in efforts to capture spillovers abounds. Nadiri (1993)
reports that a significant proportion of R&D conducted in the U.S. is done by foreign
firms--possibly attempting to counteract any geographic spillover disadvantages. Nadiri
also reports an increase in recent years of joint ventures in R&D. One motive for these
ventures is to internalize potential spillovers. Henderson and Cockburn (1995) provide
evidence that economies of scope in the pharmaceutical industry may be generated by
The implication of this behavior is that there may not be as much of a role for
strategic industry policy based on spillovers as popularly conceived. Firms will
inevitably have superior information about the magnitude and direction of potential
spillovers than the government (or economists) and will incorporate this information into
their decisions. The market imperfections associated with knowledge production and
dissemination may not be as large as commonly believed, at least in well developed
This chapter is concerned with the meaning and measurement of international
intraindustry R&D knowledge spillovers. Because there seems to be some confusion in
the literature as to the precise nature of R&D knowledge spillovers, I spend some time
discussing the concept. I develop an equation of knowledge accumulation through
innovation and costly technology transfers from abroad. This is compared to existing
efforts to detect international spillovers of knowledge. I conclude that many existing
'7Thompson (1995a) looks at the consequences of industrial espionage and piracy for
international relations. He cites the example of Chinese firms illegally producing bootleg
compact disks and computer software, infringing on U.S. firms' copyrights. He points
out that the gravity of the situation is due to the implicit involvement of the Chinese
government in a 'policy of piracy.'
measures of spillovers are biased and that spillover-seeking behavior by firms engaged
in R&D lowers the magnitude of ex ante spillovers.
Future work includes testing the knowledge accumulation equation developed in
the paper to see if it improves over existing studies in measuring the relative importance
of technology transfers from abroad. It also remains to endogenize innovation to
innovation spillovers, both intra and interindustry, and attempt to ascertain their avenues
of transmission and magnitudes. Finally, it may be useful to develop a model in which
these spillover magnitudes are possibly affected by the avenue of international
Research sometimes poses more questions than it answers: mine is no exception.
Chapter 1 briefly addressed the question of whether there are long-run diminishing
returns to R&D. Of course, a lifetime of research may not answer this question, but it
is still worth asking. Sustained long-run growth is an important goal of many peoples.
This dissertation represents an increment of knowledge, however small, in understanding
this process and may even generate spillovers to future work. My efforts center on the
distinction between R&D activities focused on bringing about major breakthroughs
(innovative) and those directed at duplicating existing products or processes (imitative).
This distinction, when introduced by Segerstrom (1991) into the quality ladders
model of Grossman and Helpman (1991b), provided an interesting opportunity to e\plore
the art of modeling. In Chapter 2. I showed that sufficient instantaneous diminishing
returns to each R&D activity (innovative and imitative) are necessary for stability and
'normal' comparative statics in Segerstrom's model. There is considerable empirical
supportt for the existence of diminishing returns to R&D. but it is not clear whether
innovative and imitative costs are determined separately, as implied by the model. If
innovation and imitation require separate skills, their relative intensities could be affected
by differential subsidy.
More possibilities for new research are uncovered in Chapter 3. The international
transfer of technology and its influence on trade patterns among advanced countries are
the subject of that chapter. Considerable generalization of the model is possible. The
R&D technology used is rather limiting because it implies that unit costs are determined
at the global level. If different technologies are used, allowing R&D unit costs to be
determined at the national level, trade patterns can be analyzed when FPE doesn't hold.
Can a range of relative endowments be determined for which the collusive equilibrium
can be sustained, even with small wage differentials?
Another useful endeavor is to introduce alternative avenues (to imitation) of
international technology transfer and explore the effects of policy on the relative
importance of these different avenues. Costly DFI can be introduced, as can the
possibility of licensing. In a model of process innovation, for example, is the magnitude
of potential spillovers maximized through encouraging DFI, imitation. or some
combination? Does the answer depend upon the degree of similarity between the relevant
countries' tecIlhnoIly \ bases?
This last question leads to yet another implication of the model of Chapter 3. The
assumption of an exogenous learning-by-doing effect, by which imitative R&D plays a
vital role--not just in diffusing current technology, but in refining the research techniques
vital for future innovation--begs for formal modeling. There are dual aspects to this
learning. First, for the successful finn (or country). and, to a lesser extent, all engaged
in the imitation race, achieving the end product--knoit ledge--allows the firm (or country)
to travel closer to the technology frontier. This would seem to be a necessity if the firm